Can anyone give me a hint on how to approach this problem? It's another problem from an old qualifying exam.

Suppose that $f\colon \mathbb R \to \mathbb R$ is nondecreasing, $\int\_{\mathbb R} f' = 1$, $f(-\infty) = 0$, and $f(\infty) = 1$. Prove that $f$ is absolutely continuous on any interval $[a,b]$.