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Let $g$ be Riemann integrable on $[a,b]$, $f(x)=\int_a^xg(t)dt$ for $x∈[a,b]$.

How to show that the total variation of $f$ is equal to $∫_a^b|g(x)|dx$?

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closed as off topic by Douglas Zare, Willie Wong, Pietro Majer, Michael Renardy, George Lowther Jun 2 '12 at 10:51

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I think it's good to mention that this is also posted on Math SE:… –  Dylan Moreland May 31 '12 at 5:58
But all the Answers on SE have bug. –  Leitingok May 31 '12 at 6:07