Area using Parametric Equations

Homework Statement

Notice the curve given by:
f(t) = x = 36-t^2
g(t) = y = (t^3)-25*t
The curve makes a loop which lies along the x-axis. What is the total area insde the loop.

Homework Equations

Integral from alpha to beta of g(t)*f'(t) dt

The Attempt at a Solution

Ok, so I can easily plug in g(t) and f'(t) into the formula to find the integral. The problem is, I don't understand how to find alpha and beta. I know that if I find where t intersects itself, then I could the alpha and beta. But how do I know where t intersects itself? Please help me out!