It would depend on the wording of your insurance policy contract if you are required to report the incident but generally all accidents should be reported to your insurance company. It is wise to have your insurance company be aware of the situation so that if the at-fault's insurance company decides not to pay on the claim your insurance can help you.

In general, insurance rates do not increase unless your insurance carrier has to pay out on a claim. By reporting the accident to your insurance company you will help protect their financial interests.