The parabolas $x = y^2$ and $x = 2 - y^2$ enclose the shaded region in the figure. What is its area?

Fig. 1: Two parabolas that open sideways. The blue one is x = y squared and opens to the right. The orange one is x = 2 - y squared and opens to the left. They cross at the red dots (1, 1) and (1, -1). The lens-shaped region between them is shaded.