Truthfully, I would say "Law"- if a person is said to have integrity for having done the "right" thing, they might be considered just for having upheld the law. A person who is just yet does not have integrity might be said to follow the letter of the law, and not the spirit.

Actually, I think of integrity as being or staying truthful, in words or to oneself and others. People with integrity do what they say they are going to do, they come through where they promised they would- if that involves upholding the law, or ensuring impartial fairness then we can call them just as well. ...just as well, really.... (sorry, couldn't resist)

Truthfully, I would say Law – if a person is said to have integrity for having done the "right" thing, they might be considered just for having upheld the law. A person who is just yet does not have integrity might be said to follow the letter of the law, and not the spirit.

Actually, I think of integrity as being or staying truthful, in words or to oneself and others. People with integrity do what they say they are going to do, they come through where they promised they would – if that involves upholding the law, or ensuring impartial fairness then we can call them just as well.
… just as well, really …  
(sorry, couldn't resist)