Let $f$ be an increasing function defined on $[a,b]$ and let
$a < x_1 < x_2 < \ldots < x_n < b$ be $n$ points in the interior of $[a,b]$
Show that $\sum_{k = 1}^n\left[f(x_k^+) - f(x_k^-)\right]\leq f(b^-) - f(a^+)$
The proof I have is very wordy and sketchy. I know it would be easier if I could find a telescoping sum but I've got a road block in my mind. :/