Moral: concerned with the principles of right and wrong behavior and the goodness or badness of human character.
Integrity: the quality of being honest and having strong moral principles; the state of being whole and undivided.
It can be explained as the belief in their own moral ethics and the conviction to stick by them even during times of adversity and misfortune. Therefore, a person who is capable of sticking to his ethics even during hard times is said to have moral integrity.