Integrity is a big thing and Character is just a subset. If you go by the actual meaning of Integrity...I don't think most of us have any integrity. Integrity consist of:
1) To be true to yourself and people around you.
2) To keep your words...your commitment.
3) Walk the talk.
4) Respect for yourself and people around you.
5) Be modest and be humble.
6) Don't cheat...don't lie.
7) Your principles, your values and your ethics.
If you just look at "Character"...it consist of your "BEHAVIOUR" and the way you carry yourself in public.
Related to Character...there are two terms..."Loose Character" and "Character Assassination". We are social animal and we cannot exist in isolation. Just like, there are rules for every game...there are rules to live in the society. And if any one behaves in a manner which is not permissiable by social norms...that person is called as a person with "Loose Character". Few Examples...
1) Kissing your partner at public places.
2) Beating or abusing your partner at public places.
3) Married and still having relations outside marriage...or not married but having relation with someone who is married.
All the above mentioned...as per social norms...are termed as traits of loose character...there can be more examples.
"Character Assassination" is a term used...when you talk about something about somebody in his or her absence. Example...Ram JethMalani in Jessica Lal Case. In short, talking something bad about the person in his or her absence, when they cannot defend themselves.
I hope this will help.
Regards
Sanjeev Sharma
(Blog:
http://sanjeevhimachali.blogspot.com/)