Answer
$\dfrac{8}{3}$
Work Step by Step
Here, the area can be expressed as: $A=\int_{-1}^{1}[x^2-(-1)] \ dx=\int_{-1}^{1} (x^2+1) \ dx$
In order to solve the above integral, we will use the following formula such as:
$\int x^n \ dx=\dfrac{x^{n+1}}{n+1}+C$
Now, we have $\int_{-1}^{1} (x^2+1) =[\dfrac{x^3}{3}+x]_{-1}^{1}$
or, $=[\dfrac{1^3}{3}+1]-[\dfrac{(-1)^3}{3}+(-1)]$
or, $=\dfrac{4}{3}-(-\dfrac{4}{3})$
Therefore, the required area is: $Area=\dfrac{8}{3}$
