Let $f(s,u)$ be a deterministic function. Consider the stochastic integral
$$ X_t = \int_0^tf(t,s)\,dW_s\quad(1). $$
I want to use the integration by part formula
$$ X_t^2 = X_0^2+2\,\int_0^tX_s\,dY_s+[X,X]_t $$
but since the extreme of integration in $(1)$ also appears inside the integration I am a little bit confused on how to apply it.