Integration of a function in a manifold

Question

Let $M$ be a complete Riemannian manifold and $u$ be a smooth function. Suppose there is a constant $K>0$ such that $$\int_{B_r(p)}(K+u)dV=0, \ \forall 0\leq r<\infty,$$where $B_r(p)$ is the ball with center $p\in M$ and radius $r$. From the above inequality can we conclude that $u=K$? Please anyone help.
Thank you.