It has nothing to do with "integrity." If any of you have ever observed yourself violating a traffic rule or law, or for that matter anything that violates the rules and laws of your community, town, state, and country, and failed to turn yourself in demanding to pay the consequences, then you too must be lacking in integrity. Observed your wife, relative, or friend doing this and you didn't report them? Same thing.
For every rolling stop you ever did. For any jaywalking or being 1 mph over any posted speed limited. Driving with a head light or brake light out no matter how short the time frame. If you did not immediately pull your car off the road and seek out emergency assistance for a tow or repair, you lacked integrity.
Ever ran through a stop sign in a strange area that you just didn't see? Or went down a one way street that you were unfamiliar with? I've done that multiple times. If you didn't immediately seek out a police officer to write you up you lacked integrity, more so than the OP who was actually caught in the act. You violated the law and did nothing to rectify it to the community.