I have difficulties with the following exercise:
Given W a Brownian motion, $T > 0$ and $H = \int_0^T W_u^2 du,$ the task is to find a function g such that: $$H = \mathbb{E} [ H ] + \int_0^T g(u, W_u) dW_u$$
Do you have any hints? I have tried writing the integral that defines $H$ as Riemann sums and then play around, but I managed nothing.
Hint: try applying Ito's formula to $$ X_t=(T-t)W_t^2$$