Mold in bedroom: leaking tub?

We were just removing wood trim around our bedroom to change out the flooring, and we found mold in two corners of the room. One of the corners is next to the tub and is damp, and the other is near the window and is dry. It seems that at a minimum our tub is leaking. There are a few small hairline cracks in the tub that I can see. Is there a good way to identify if that is the issue, and what are the next steps? I’m in Santa Cruz CA, attaching photos of both spots with mold and the tub