I have a stopping time $\tau$ and a stochastic process $f$.
Then the following equation is true:
\begin{equation} \int^{t\wedge\tau}_{0}f(s)dW(s)=\int^{t}_{0}f(s)\chi_{[0,\tau]}(s)dW(s) \end{equation}
Can someone explain why isn't it trivial as it is with a 'normal' Riemann integral?