Is $750 to repair roof damage a fair price?

I am a first-time homeowner. My neighbor pointed out some damage on my roof, which I believe occurred during recent storms. There is also concern that a raccoon may be involved. I was previously told the roof had a couple of years left. I am trying to decide whether to use a contractor for this repair or file an insurance claim, especially since I'm unsure if insurance covers raccoon damage. I cannot afford a full roof replacement at this time. I have temporarily covered the damage with a tarp.