On a lecture notes, there is a following arguement: To make $\int_0^T \pi_t dW_t$ well-defined, (maybe it means to make $\int_0^T \pi_t dW_t<\infty \ \ a.s.$) we only need $\int_0^T \pi_t^2 dt<\infty$. Where $W_t$ is a standard one dimention Brownian Motion, $\pi_t$ is a previsible process.
Question: I don't understand how we can use condition $\int_0^T \pi_t^2 dt<\infty$ to make the stochastic integral well-defined. Do we need to add some other conditions??