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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.

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

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

I know, by a theorem, that S(f)

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

## Homework Statement

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]?## Homework 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]}## 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.

## Homework Statement

## Homework Equations

## The Attempt at a Solution

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