8/3
1) Let's calculate this area by using Integration. We have two functions:
[tex]f(x)=x^2,g(x)=-1[/tex]
2) So let's plot them to better visualize it:
Note that we have to find the area between two curves, considering from x=-1 to x=1, so let's integrate, considering f(x) > g(x):
[tex]\begin{gathered} A=\int ^1_{-1}(f(x)-g(x))dx \\ A=\int ^1_{-1}(f(x)-g(x))dx \\ A=\int ^1_{-1}x^2+1dx \\ A=\int ^1_{-1}x^2dx+\int ^1_{-1}1dx \\ A=\frac{2}{3}+2=\frac{8}{3} \end{gathered}[/tex]
3) Hence, the area between those curves is 8/3
