What are you asking for in the first question? It looks to me like you want a closed form expression for the summation? ( (n+1)(2n+1)/(6n^2) )
The integral has nothing to do with x, so the limit does not exist. I'm having a hard time understanding why this question was asked because the answer is too simple.
I can give you a hint as to how to do the integral (sub b = x*sec(theta)), but what do you mean by a graph? The integral is a real number.