For there to be a region bounded by the two parabolas, you first need to find some conditions on 
. The two parabolas must intersect each other twice, so you need two solutions to
You have
which means you only need to require that
. With that, the area of any such bounded region would be given by the integral
since
for all . Now,
by symmetry across the y-axis. Integrating yields
![=4\left[c^2x-\dfrac{16}3x^3\right]_{x=0}^{x=|c|/4}](https://tex.z-dn.net/?f=%3D4%5Cleft%5Bc%5E2x-%5Cdfrac%7B16%7D3x%5E3%5Cright%5D_%7Bx%3D0%7D%5E%7Bx%3D%7Cc%7C%2F4%7D)
Since
, you have 
.
You have
which means you only need to require that
since
by symmetry across the y-axis. Integrating yields
Since
