Integrity literally means to be whole ( from the Latin word integer). It’s not simply about doing the right thing, because as another respondent noted, one can be faced with a situation in which any decision may cause harm. When a person is whole, though, his actions are connected to his values,

When a person is psychologically fragmented, which we all tend to be to some extent, his behaviors are more outwardly oriented, because his internal compass is damaged. So what really matters is how we respond under stress. Is it according to our values or according to what is expedient or popular?

And then, of course, is the person even aware of his values? Have you identified yours?