The following parametric equations trace out a loop. $$\begin{array}{r@{\,}c@{\,}l} x & = & 5-\frac{2}{2} t^2 \cr y & = & -\frac{2}{6}t^3+ 2 t + 1 \end{array}$$ Find the $t$ values at which the curve intersects itself:
$t = \pm$ .
What is the total area inside the loop?
Area = .