Let $A$ and $B$ be two sets defined in the Cartesian plane as follows: $A = \{(x, y) \in \mathbb{R}^2 : y \geq x^2 - 1\}$ $B = \{(x, y) \in \mathbb{R}^2 : y \leq 1 - x^2\}$ Determine the area of the region represented by the intersection $A \cap B$.