Integral of an interior product is 0

Question

Here is a question about problem 3.12 from Do Carmo's Riemannian Geometry. $M$ is a compact orientable and connected Riemannian $n$ manifold. $f$ is a differentiable function on $M$ such that $\Delta f\ge 0$.Let $X$ be the gradient of $f$. $v$ is the volume form on $M$ and $i(X)v$ denotes the interior product of $X$ and $v$. We want to show $\Delta f=0$. In the hint given by him, there is an identity $$\int_M\ \Delta fv=\int_MdivXv=\int_M d(i(X)v)=\int_{\partial M}i(X)v=0$$ Where $div Xv= d(i(X)v)$ is obtained in a previous problem. The third equality is by Stokes theorem. I have no idea why the last equality holds. Any help will be appreciated.