Can someone please help me prove this? I've tried it to work it out in different ways and I'm beat. Will appreciate your help.

The problem reads:

Let be a continuous function on . The length of the curve on the interval is defined by

(don't know how to the _P under the sup)

where

and the supremum is taken over all partition points of .

Assume that has continuous derivative on . Take any partition of and derive

.

Next, use the Mean Value Theorem, and then use the definition of the Reimann integral to establish that

.

Thank you so much for your help.