Mathematics

Problem

Let

f(x)=x+2

and

g(x)=x^{2}

. The graphs of

f

and

g

intersect at

x=-1

and

x=2

. Which of the following definite integrals equals the exact area of the region enclosed by the two graphs between these points of intersection? a)

\displaystyle\int_{-1}^{2}\bigl(x^{2}-(x+2)\bigr)\,dx

\displaystyle\int_{-2}^{1}\bigl((x+2)-x^{2}\bigr)\,dx

\displaystyle\int_{-1}^{2}\bigl((x+2)-x^{2}\bigr)\,dx

\displaystyle\int_{-1}^{2}\bigl((x+2)+x^{2}\bigr)\,dx