Can you go from the integral of x squared to the summation of x squared? To be specific, I was wondering if you could go from the indefinite integral of $x^2$, mainly
$\int$ $x^2$$dx = \frac{x^3}{3}$, to the summation of $x^2$, $\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$?

The difference between the integral and the actual sum is the difference of $n^3/3$ and $\frac {n(n+1)(2n+1)}{6}$ that is $$\frac{(n+1)^2}{6}$$ 
Which grows very fast with $n$ 
