If second distributional derivative of $f$ is zero, what kind of a function is $f$?

Question

Given a continuous function $f$ such that $\int f(x)\phi''(x) =0 $ for all $\phi$ $\epsilon$ $D(R).$

Then what can we say about $f$? The problem is straightforward if $f$ $\epsilon$ $C^2$ Kindly provide an answer with a proof.