$\int_{\mathbb{R}}\mu((A-x) \cap B)d\mu = \mu(A)\mu(B)$

Question

Given two measurable subsets $A, B$ of $\mathbb{R}$, I want to show that $\int_{\mathbb{R}}\mu((A-x) \cap B)d\mu = \mu(A)\mu(B)$, where $A-x = \{a-x : a \in A\}$ and $\mu$ is the Lebesgue measure on $\mathbb{R}$. All I can think of is that $\mu(A) = \mu(A-x)$, because that's just translation, and that I might somehow set up an integral to use the Fubini theorem for this one, since the product $\mu(A)\mu(B)$ is in the equation. But I don't know where to go from here.