$M > 0$ such that for any partition $\{x_0, ... , x_n \}$ of $[a, b]$, $ \sum_{k=1}^{n}\dfrac{|F(x_k)-F(x_{k-1}|^p}{|x_k-x_{k-1}|^{p-1}}\le M.$

Question

For $1 < p < \infty$, show that if the absolutely continuous function $F$ on $[a, b]$ is the indefinite integral of an $L^P[a, b]$ function, then there is a constant $M > 0$ such that for any partition $\{x_0, ... , x_n \}$ of $[a, b]$,

$$ \sum_{k=1}^{n}\dfrac{|F(x_k)-F(x_{k-1})|^p}{|x_k-x_{k-1}|^{p-1}}\le M.$$

I am not getting clue to do the problem. Help Needed.