Answer
$2$
Work Step by Step
Here, the area can be expressed as: $A=\int_{-1}^{1}[x^3-(-1)] \ dx=\int_{-1}^{1} (x^3+1) \ dx$
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 $\int_{-1}^{1} (x^3+1) =[\dfrac{x^4}{4}+x]_{-1}^{1}$
or, $=[\dfrac{1^4}{4}+1]-[\dfrac{(-1)^4}{4}+(-1)]$
or, $=\dfrac{5}{4}-(-\dfrac{3}{4})$
Therefore, the required area is: $Area=2$
