I need to find the expression for variance of the integral with the following form:
$\int_0^T X_tdW_{2t}$
when $X_t=f(W_{1t})$ and both $W_{1t}$ and $W_{2t}$ are defined on the same sample space and are correlated. More specifically, is it still possible to use (a version of) Ito Isometry that would take the correlation into account?