Proving a function of bounded variation is Riemann Integrable

[ECmathstudent]

Homework Statement

If a function f is of bounded variation on [a,b], show it is Riemann integrable

Homework Equations

Have proven f to be bounded

S(P) is the suprenum of the set of Riemann integrals of a partition (Let's say J)
s(P) is the infinum of J

S(P) - s(P) < e implies f is Riemann integrable

The Attempt at a Solution

I know I'm supposed to set up two partitions, one regular one and one so that for each second piece of the partition:
f(a i) >= Mi - c
f(a i+1) =< mi -c

This will give a new sum, and I'm supposed to use this to show that S(P) - s(P) is less than epsilon. Sorry I don't know how to use Latex!

 

[ECmathstudent]

A nevermind, I've got it.