In the classroom my teacher stated that the Gauge-fixing term in the action $$\frac{1}{2\alpha}\int d^4x (\partial_\mu A^\mu(x))^2$$ transforms under $A_\mu(x) \rightarrow A_\mu(x)+\partial_\mu \theta(x)$ as: $$\frac{1}{\alpha}\int d^4x(\partial_\mu A^\mu(x))(\partial_\nu \partial^\nu \theta(x))$$ when inserting the transformation in the first equation I get the additional term: $$\int d^4x (\partial_\mu\partial^\mu \theta(x))^2.$$ I was wondering why this term is null; any hint is appreciated.
EDIT: It was an infinitesimal transformation: with $\theta$ small higher order of $\theta$ were discarded.