Film capacitors, replacing with ceramics
MLCC capacitors, especially of large values, are notoriously voltage dependent so NO, I would never use one of them for an integrator if you care about the precision of your time constants. Typical dynamic capacitance of these capacitors can drop to as little as 30% of their nominal value by the time you have reached half of their rated voltage.

Also, be very careful not to crack it by bending your PCB even slightly, as when inserting connectors. Don't place them anywhere near a board edge that will be removed. If removing board edges, please don't use priers (!).

I use MLCC capacitors for decoupling supplies and to get scared. Their failure mode is typically a short-circuit. Presumably, in your application, a short-circuit means run-away heating in your control loop.