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Advanced Calc

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Sorry, guys, this isn't abstract but the calc board didn't seem very active... I could really use the help on this one...

 

Prove:

f(x): [a, b] ----> R has f'(x) continuous @ each x in [a,b] then the definite integral from a to b exists

 

Could someone please make a proof for this one? I am lost as to what to do.

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