"Integrity is the recognition of the fact that you cannot fake your consciousness, just as honesty is the recognition of the fact that you cannot fake existence - that man is an indivisible entity, an integrated unit of two attributes: of matter and consciousness, and that he may permit no breach between body and mind, between action and thought, between his life and his convictions - that, like a judge impervious to public opinion, he may not sacrifice his convictions to the wishes of others, be it the whole of mankind shouting pleas or threats against him - that courage and confidence are practical necessities, that courage is the practical form of being true to existence, of being true to truth, and confidence is the practical form of being true to one's own consciousness."
"Integrity does not consist of loyalty to one's whims, but of loyalty to rational principles."
"The virtue involved in helping those one loves is not "selflessness" or "sacrifice," but integrity. Integrity is loyalty to one's convictions and values; it is the policy of acting in accordance with one's values, of expressing, upholding and translating them into practical reality. If a man professes to love a woman, yet his actions are indifferent, inimical or damaging to her, it is his lack of integrity that makes him immoral."
~ Found at Ayn Rand Lexicon - Integrity