It is proved that Ito stochastic integral $\int X_sdB_s$ is zero with probability one on the set on which $\int X^2_sds$ is zero. This result is used to show that, for Lipschitz continuous coefficients $a$ and $b$, diffusive process $\{X_t\}$, defined as $dXt=a(X_t)\,dB_t+b(X_t)\,dt$, and deterministic process $\{Y_t\}$, defined as $dY_t=b(Y_t)\,dt$, with the same initial values are indistinguishable up to the first exit from the domain where diffusive coefficient a is zero.