Showing a function is bounded

Question

Please why if you have a function in $BV$ then $F$ is a bounded function.

where $BV$ = { $F$: $R$ $\to$ $C$ , T$_F$($\infty$) < $\infty$ }

Answer 1

$|F(b)-F(a)| \leq T_F (b) -T_F (a)$ by definition, so F is bounded.