Integrity means never sacrificing one's convictions to the opinions or wishes of others.
Allegiance to the virtue of integrity requires always keeping in one's mind the basic principles upon which one's system of philosophy is founded. Maintaining the virtue of integrity involves never relinquishing those basic principles, no matter what the temptation or lure.
A man of integrity need fear no question of his honor, for he knows that his integrity is available for all to see, to test, and to view as sound. Do not claim that a man of integrity is without integrity, for it is in keeping with the virtue of integrity that the man censure you and lay bare your own lack of integrity.
Integrity is recognition of the fact that you cannot fake your consciousness-that man is an indivisible entity, and 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.- Ayn Rand, Atlas Shrugged