This is my first time posting & I am not familiar with how to get all the correct math symbols or how to use Latex, so I did the best I could.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Suppose f is bounded on [a,b] and there is a partition P* of [a,b] for which S(f,P*)=S(f,P*). Is f Riemann integrable on [a,b]?

2. Relevant equations

S(f)=sup{S(f,P*): P* is partition of [a,b]}

S(f)=inf{S(f,P*); P* is partition of [a,b]}

3. The attempt at a solution

I know, by a theorem, that S(f)>S(f). I am trying to figure out how to show S(f)<S(f) so that I can say S(f)=S(f). I thought about choosing another partition P_{e}such that S(f,P_{e})-S(f,P_{e}) would equal some epsilon value, but I don't know what value I should use or where to go next.

If this is the wrong process for this proof, I would love a hint on where to start.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: If supremum=infimum, is f Riemann integrable?

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