Integral of a covariance function

Question

Let a covariance function be $COV(y(X),y(X'))=R(X,X')$ and $\mathbf{E}_{y}^{Q}=\int\limits_{X_Q} y(X)\ dX_Q$, in which $X_Q$ is a subset of $X$. Why does $COV(\mathbf{E}_{y}^{Q},y(X'))=\int\limits_{X_Q}R(X,X')dX_Q$ hold? Does anyone give me a hand to explain that equation? Ths.