Derivation of Coulomb's law from classical field theory

In the section on Coulomb’s law in QFT by Schwartz, he expands $-frac{1}{4}F_{munu}^{2}$ to get $-frac{1}{2}(partial_{mu}A_{nu})^{2} + frac{1}{2}(partial_{mu}A_{mu})^{2}$, can someone please explain how he arrives at the second term in this expression? I am getting this term as $frac{1}{2}(partial_{mu}A_{nu})(partial_{nu}A_{mu})$.