If $B_t$ denotes a standard Brownian motion, and let $X_T = \int f(s)dB_s$, f(s) is a deterministic integrand. I known $B_t$ is a martingale, Is $X_T$ also a martingale? And how can i get the formula of moment statistics of X, say, $E(X_t^2)$ , $E(X_t^3)$?