## bounded variation

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

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

(where $T$ 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.