show integrability of random variable

Question

Let $X_1,X_2,\ldots$ be iid random variable with $E[X_i]=0$ and $P(X_i>0)>0$. Let $S_0=x>0$ and define $S_n=S_0+\sum_{i=1}^nX_i$. Then define $T=\inf\{n \geq 0: S_n \leq 0 \text{ or } S_n \geq b\}$. I have shown that $T$ has finite expectation, and am trying to show $X_T$ is integrable. Any hint or help would be great!