Proof finite stopping time and Wiener process bounded

Question

Let $T_{-a,b}=\inf\{t\geq 0: W_{t} \notin [-a,b]\}, a,b>0$.

I want to show that this is a finite stopping time ($P(T_{-a,b}<\infty)=1$) and that $|W_{\min(T_{-a,b},t)}|$ is bounded by a constant. Can anyone help me with this? I really don't see it. Thanks!