This is where your Home Inspector comes in. Depending on the span distance, HOPEFULLY, the current or previous owner didn't remove a Lolly Column, or the like, where it is suppose to hold up the span! The floor may or may not be safe. The Inspector needs to look for 'signs' of a weight bearing wall (down below) and the possible placement of a Column.
At the same time, your situation may be just age. Your joists may be sagging for a variety of reasons. Have the home inspected since we can't see it from here. Your 'problem' may simply require re-screwing the sub-floor, adding shims, adding a Column, replacing a 'bad joist', among others.
Other Follow-uppers may have more to add. My best to ya and hope this helps.