"...It must be Willoughby therefore whom you suspect. But why? Is he not a man of honour and feeling? Has there been any inconsistency on his side to create alarm? can he be deceitful?"
"I hope not, I believe not," cried Elinor. "I love Willoughby, sincerely love him; and suspicion of his integrity cannot be more painful to yourself than to me. It has been involuntary, and I will not encourage it...."
Lucy was naturally clever; her remarks were often just and amusing; and as a companion for half an hour Elinor frequently found her agreeable; but her powers had received no aid from education: she was ignorant and illiterate; and her deficiency of all mental improvement, her want of information in the most common particulars, could not be concealed from Miss Dashwood, in spite of her constant endeavour to appear to advantage. Elinor saw, and pitied her for, the neglect of abilities which education might have rendered so respectable; but she saw, with less tenderness of feeling, the thorough want of delicacy, of rectitude, and integrity of mind, which her attentions, her assiduities, her flatteries at the Park betrayed; and she could have no lasting satisfaction in the company of a person who joined insincerity with ignorance; whose want of instruction prevented their meeting in conversation on terms of equality, and whose conduct toward others made every shew of attention and deference towards herself perfectly valueless.
...Had Edward been intentionally deceiving her? Had he feigned a regard for her which he did not feel? Was his engagement to Lucy an engagement of the heart? No; whatever it might once have been, she could not believe it such at present. His affection was all her own. She could not be deceived in that. Her mother, sisters, Fanny, all had been conscious of his regard for her at Norland; it was not an illusion of her own vanity. He certainly loved her. What a softener of the heart was this persuasion! How much could it not tempt her to forgive! He had been blamable, highly blamable, in remaining at Norland after he first felt her influence over him to be more than it ought to be. In that, he could not be defended; but if he had injured her, how much more had he injured himself; if her case were pitiable, his was hopeless. His imprudence had made her miserable for a while; but it seemed to have deprived himself of all chance of ever being otherwise. She might in time regain tranquillity; but HE, what had he to look forward to? Could he ever be tolerably happy with Lucy Steele; could he, were his affection for herself out of the question, with his integrity, his delicacy, and well-informed mind, be satisfied with a wife like her—illiterate, artful, and selfish?
Mrs. Jennings was very warm in her praise of Edward's conduct, but only Elinor and Marianne understood its true merit. THEY only knew how little he had had to tempt him to be disobedient, and how small was the consolation, beyond the consciousness of doing right, that could remain to him in the loss of friends and fortune. Elinor gloried in his integrity; and Marianne forgave all his offences in compassion for his punishment. But though confidence between them was, by this public discovery, restored to its proper state, it was not a subject on which either of them were fond of dwelling when alone. Elinor avoided it upon principle, as tending to fix still more upon her thoughts, by the too warm, too positive assurances of Marianne, that belief of Edward's continued affection for herself which she rather wished to do away; and Marianne's courage soon failed her, in trying to converse upon a topic which always left her more dissatisfied with herself than ever, by the comparison it necessarily produced between Elinor's conduct and her own.
Elinor had heard enough, if not to gratify her vanity, and raise her self-importance, to agitate her nerves and fill her mind;—and she was therefore glad to be spared from the necessity of saying much in reply herself, and from the danger of hearing any thing more from her brother, by the entrance of Mr. Robert Ferrars. After a few moments' chat, John Dashwood, recollecting that Fanny was yet uninformed of her sister's being there, quitted the room in quest of her; and Elinor was left to improve her acquaintance with Robert, who, by the gay unconcern, the happy self-complacency of his manner while enjoying so unfair a division of his mother's love and liberality, to the prejudice of his banished brother, earned only by his own dissipated course of life, and that brother's integrity, was confirming her most unfavourable opinion of his head and heart.
The word 'integrity' shows up once in Persuasion, once in Northanger Abbey, once in Emma. It does show up three times in Pride and Prejudice and four times in Mansfield Park, but I think there's a good argument that, while not unimportant, the idea simply does not play as important a role in the actual plot of either work. It does play a crucial role in Sense and Sensibility, however: Lucy Steele's lack of integrity, which is specifically highlighted, is an essential plot point, of course, but much more importantly, the bulk of the actual story of SS is concerned with the two ongoing questions of Willoughby's integrity and Edward's integrity. Perhaps the key evidence, though, is that we get continual reference to the opposite of integrity, this active insincerity or deceitfulness.
I think it's probably significant that there is never any question of the integrity of either heroine -- Elinor, of course, is practically integrity in female form, and, no matter what criticisms can be made of Marianne, insincerity or deceitfulness is not one of them. I also suspect that there's a close connection between the theme of integrity and the repeated return to aesthetic topics in the novel (see, for example, Marianne's comments on the picturesque in Chapter 18, especially the criticism of those for whom talk of the picturesque becomes mere jargon).