I do not understand the following result:
Suppose $dz_\chi$ and $ dz_\xi$ are correlated increments of standard Brownian motion with $dz_\chi dz_\xi=\rho dt$ you have the following expectation giving the following result:
$\mathbb{E} [\int_{t}^{T}e^{\kappa s} dz_\chi \int_{t}^{T}dz_\xi] = \rho \int_{t}^{T}e^{\kappa s} ds$
I really do not get it. This equation is justified by the Itô's isometry. In the book that I am reading the author just passes by saying that is easy to see, but if someone could show more explicit the steps that are taking to get this equation.