Answer
$\dfrac{7}{3}$
Work Step by Step
Let us consider that two continuous functions $f(x)$ and $g(x)$ with $f(x)\geq g(x)$ on the interval $[a,b]$ . The area (A) of the region bounded by the graph of $f(x)$ and $g(x)$ on the interval $[a,b]$ can be calculated as: $Area(A)=\int_a^b [f(x)-g(x)] \ dx$
Thus, the area of the region is:
$A=\int_a^b [f(x)-g(x)] \ dx= \int_{-1}^{0} (2+x-x^2) \ dx+\int_{0}^{1} (2-x-x^2] \ dx \\=[2x+\dfrac{x^2}{2}-\dfrac{x^3}{3}]_{-1}^{0}+[2x-\dfrac{x^2}{2}-\dfrac{x^3}{3}]_0^1 \\=[0-(2(-1)+\dfrac{(-1)^2}{2}-\dfrac{(-1)^3}{3})]+[(2)(1)-\dfrac{1}{2}-\dfrac{1}{3}]\\=\dfrac{7}{3}$
