How to expand x^3 in integrals?

I have the integral from 1 to 2 of x^3dx. I know that doing it using the fundamental theorem of calculus is a cinch, but I need to learn to do it the long way (lim n-> inf etc). So in order to do that, I need to know, how can I expand in x^3, because I've totally forgotten. I need to expand (2 + (i/n) )^3. Your help will be appreciated and rewarded. Oh and remember "i" is not an imaginary number, it's a variable just like n.