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Real Analysis on Integration Problem

I need a correct and concise solution. If the answer is not 100% correct, I will ask for my money back!

We just finished integration and are done
with a first course in analysis, i.e. chapters 1-6 of
Rudin. We are also using the Ross and the Morrey/Protter
book.

The Problem:

f : R --> R , f ' ' ' ' continous.

FIND ALL FUNCTIONS THAT SATISFY THE FOLLOWING:

S (from a to b) f (t) dt = [(b - a) / 6] ( f(a) + f(b) + 4 f( (a+b) / 2) )

for all a, b in R.

f ' ' ' ' means four times differentiable.
S means the integral

Solution Summary

A Real Analysis Problem is solved.

$2.19