I have the following definition of MSE which is defined using the Expectation. When this expectation is applied to the inner parts a Variance comes out and I just miss which rule has been applied. The context of this is estimating the distribution of the MSE in nonparametric density estimation:

MSE(X)=\mathbb{E}[(\hat{f}(x)-f(x))^2]=(\mathbb{E}[\hat{f}(x)] - f(x))^2+Var(\hat{f}(x))

Thanks in advance,
Best regards,