How do I do these Calculus Problems?

I need to make an integral that works for all of this...

(1^2+2^2+3^2+4^2+...+n^2)/(n^3)

I need to find the limit as x approaches 5 of this: (2x/(x-5)) x the integral of [sin(t)]/t dt.

I think this has something to do with as f(a)-f(x)/(a-x)=f'(a) or something like that.

Last one I need help on is the integral of square root of (b^2-x^2) db from the interval (b/square root of 2) to b. I need to show the graph without using a calculator or at least show where it should be.

You don't have to answer all questions but 1 would be nice.