Assume we have two integrated Brownian Motions
$\int_0^tf(t)dW_t$ and $\int_0^tg(t)dY_t$
where the $d$-dimensional Brownian Motions $W$ and $Y$ are correlated according to the positive semi-definite matrix $C$
$dW_tdY_t=Cdt$
I am trying to calculate the Covariance process of the sum of these two integrals. So far I have
$<\int_0^tf(t)dW_t+\int_0^tg(t)dY_t,\int_0^tf(t)dW_t+\int_0^tg(t)dY_t>\\ =\int_0^tf^2(t)dt+\int_0^tg^2(t)dt+2<\int_0^tf(t)dW_t,\int_0^tg(t)dY_t>$
Now my question is how the last expression looks like?