Uniqueness of the integrand of a stochastic integral

Question

Given a progressively measurable processes $\Delta_s(\omega),\Delta'_s(\omega)$ and real numbers $z',z$, there was a claim that if $$\int_0^T(\Delta_s-\Delta's)\mathrm{d}X_t=z-z'$$ for a non-trivial local martingale $X$, then $\Delta_s=\Delta'_s$. (All equal is meant to be in almost surely sense). I don't see why it is follows. Any hint are appreciated.