I'm having some trouble with the following problem:
Let $N(f;y) = |f^{-1}(y)|$ be number of $x \in [a,b]$ such that $f(x) = y$. Show if $f$ is of bounded variation, then $$\int_\mathbb{R} N(f;y) dy \leq TV(f)_a^b$$ where $TV(f)_a^b$ is total variation of $f$. The equality holds if $f$ continuous.
how should I start this problem?