Originally Posted by
vince Integration without bounds is equivalent to solving for an antiderivative.
Antiderivative of functions of the form, $\displaystyle f(x)=x^n \;where\; n\; is\; real$, amounts to
$\displaystyle Antiderivative \;of\;x^n = \int x^ndx = \frac{x^{n+1}}{n+1}+C$