If you're crawling around up there on your roof looking for a leak, you'll probably find it easily enough if you look for those curled back shingles. Check Austin roofing company to get more tips on roofing repair.
Asphalt cement is the stuff you want to use, or if you want to make things easier with a caulking gun, there is a compound you can use for this as well.
The only thing you have to worry about is if the roof shingles are dry or brittle.
If they are, they might not want to cooperate. Instead of trying to force them and making it worse to where you have to replace them, soften the shingles first. That is your roof repair tip for the day.