Comment #5 on issue 1385 by ondrej.certik: Integral.midpoint() implemented
http://code.google.com/p/sympy/issues/detail?id=1385

So maybe rather middle_sum(). How about calling it riemann_sum()

http://mathworld.wolfram.com/RiemannSum.html

and it would have a parameter method, that could have the following values:

maximum
minimum
left
right
midpoint

I have implemented the midpoint so far, the left and rigth are easy too,  
the max/min
would have to find max/min of the function on the interval, but maybe one  
can define
it as "max/min" from just three points: left, midpoint, right.

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