in my research, I need to deal with a stochastic integral with respect to a compensated poisson process, namely, $ \int_0^t f(X_t) dM_t,$ where $M(t) = N(t) - \int_0^t \lambda(s)ds$.

The integrand $f$ is bounded, and my question is do I still need $f$ to be predictable in order to make sure such integral is again a martingale.