Show that if $\displaystyle f$ is of bounded variation on $\displaystyle [a, b]$ then

$\displaystyle \int^b_a |f'| dm = T_a^b(f)$ if and only if $\displaystyle f$ is absolutely continuous.

(where $\displaystyle T$ denotes the total variation)

I know how to do the backward direction. However, I do not see how to do the forward direction right now. Any hints would be very nice. Thanks in advance.