Answer
$$A = \frac{{9152}}{{105}}$$
Work Step by Step
$$\eqalign{
& {\text{From the graph we can note that the intersection points between}} \cr
& {\text{the curves are at }}x = - 3{\text{ and }}x = 1 \cr
& {\text{The area is given by:}} \cr
& A = \int_{ - 3}^1 {\left( {3 - 2x - {x^6} - 2{x^5} + 3{x^4} - {x^2}} \right)} dx \cr
& {\text{Integrating}} \cr
& A = \left[ {3x - {x^2} - \frac{{{x^7}}}{7} - \frac{{{x^6}}}{3} + \frac{{3{x^5}}}{5} - \frac{{{x^3}}}{3}} \right]_{ - 3}^1 \cr
& {\text{Evaluate and simplify}} \cr
& A = \left[ {3\left( 1 \right) - {{\left( 1 \right)}^2} - \frac{{{{\left( 1 \right)}^7}}}{7} - \frac{{{{\left( 1 \right)}^6}}}{3} + \frac{{3{{\left( 1 \right)}^5}}}{5} - \frac{{{{\left( 1 \right)}^3}}}{3}} \right] \cr
& {\text{ }} - \left[ {3\left( { - 3} \right) - {{\left( { - 3} \right)}^2} - \frac{{{{\left( { - 3} \right)}^7}}}{7} - \frac{{{{\left( { - 3} \right)}^6}}}{3} + \frac{{3{{\left( { - 3} \right)}^5}}}{5} - \frac{{{{\left( { - 3} \right)}^3}}}{3}} \right] \cr
& A = \frac{{188}}{{105}} + \frac{{2988}}{{35}} \cr
& A = \frac{{9152}}{{105}} \cr} $$
