Question: Is there a riemann sum to integral converter?

Is there a riemann sum to integral converter?

If not then,

So I thought I could make some progress using the maple limit command in the this problem:

limit(Sum(csc(Pi*x/i)^3*sin(Pi*x)^3/i^3, i = 1 .. n), n = infinity)

which gives signum(sin(Pi*x)^3/x^3)*infinity

but what does this mean? 

How do I convert Sum(csc(Pi*x/i)^3*sin(Pi*x)^3/i^3, i = 1 .. n), n = infinity to an integral or from this result?

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