I am a permanet resident and want to apply for citizenship but was arrested and given a trespassing back in 2006 but it doesn't show on my criminal record that my company that I work for just ran. Should I report it on the application ?

Yes of course you report it, if you fail to report it, you can be denied ( and most likely will be) for lying.

It does not ask, what is showing up on report, it is asking what you were convicted of