painting my bedroom -- found drywall tape peeling?
It depends on what you want the job to look like. The tape joint has failed. It could have had a void under it, it could be stressed from settlement, water. Hard to tell, but whatever has failed has to be cut out and replaced. If it's only one side, just cut it and spackle. If it's both sides, the easy fix is to gently cut it out, spackle, sand, prime, run a bead of caulk down the corner, finish. If you insist on replacing the corner properly, that's a whole other thread.