If
$${\rm Cov}[dW_t,dB_t]=\rho dt$$
then what is
$$\mathbb{E} \left[\int_0^t\sigma_{1s}dW_s \int_0^t\sigma_{2s}dB_s\right]$$
where $\sigma_{1s}$ and $\sigma_{2s}$ are two deterministic functions of $t$?
If
$${\rm Cov}[dW_t,dB_t]=\rho dt$$
then what is
$$\mathbb{E} \left[\int_0^t\sigma_{1s}dW_s \int_0^t\sigma_{2s}dB_s\right]$$
where $\sigma_{1s}$ and $\sigma_{2s}$ are two deterministic functions of $t$?