I am asked to find $Var(aW_t+b\int_0^tf(s)W_sds)$. This is what I did until now:
\begin{align*} &\mathbb{E}\left(a^2W_t^2+2abW_t\int_0^tf(s)W_sds+b^2\left[\int_0^tf(s)W_s \, ds\right]^2 \right) \\&=a^2t+2ab\int_0^tf(s)\mathbb{E}(W_t,W_s)ds+b^2\mathbb{E}\left(\left[\int_0^tf(s)W_s \, ds \right]^2 \right) \\ &=a^2t+2ab\int_0^tf(s)sds+b^2\mathbb{E}\left(\left[\int_0^tf(s)W_s \, ds \right]^2 \right) \end{align*}
but I do not know if I am doing it correctly and how to calculate the last expectation.