Accountability means that you are held responsible for your actions and their consequences. Integrity means that you act with consistency, in general, and in relation to your professed values in specific. Depending on the professed values, one can forgive maintaining accountability and integrity, leaving the past behind

Accountability is accepting actions have consequences for which responsibly must be taken, and that the same is applicable to all people.
Integrity is a balance between personal and social obligations for the ethical protection of both.
Forgiveness is for personal peace of mind, but never forget and accept forgiveness does not excuse the offenders of accountability it simply negates the self destructive desires for revenge and allows the offended to be satisfied with justice.
It is impossible in an organized society or even in a tribal situation to answer to no one. Even those who live outside of a society are still answerable for their actions which impact either directly or indirectly on any individuals or social groups there of.

I think I need more context to answer fully. In general, I'm accountable to those with whom I interact. There's a social price to pay for deviating, though sometimes that's a price with paying, as social norms aren't necessarily ethical. Integrity is largely, for me, about setting personal standards for ethical living and then consistently working toward those goals, not living as a hypocrite, and, when I fail to live up to my ideals, to not give up on them but rather to try harder to be the embodiment of my values.

I don't know what you mean about forgiving. Can you elaborate? What do you mean about leaving the past behind?

The very powerful sometimes answer to nobody, I suppose, but I don't know exactly the question you're asking. In most societies, we all answer to the legal/justice system to some degree. In the United States, justice is supposed to be blind, but we all know that's not entirely accurate in practice.

In the end, even if I haven't answered for my actions as part of a social contract or through legal channels, I have to answer to myself. I don't have psychopathy or sociopathy, so I have to deal with the emotional consequences of my actions, and that can be worse that dealing with external accountability measures.