Answer
$$A \approx 18.759122$$
Work Step by Step
$$\eqalign{
& {\text{using a CAS we found that the intersection points between}} \cr
& {\text{the curves are at }}x = 0,{\text{ }}x \approx - 1.1080{\text{ and }}x \approx 2.5669 \cr
& {\text{From the graph we can see that the area is given by:}} \cr
& A = \int_{ - 1.1080}^0 {\left( {{x^5} - 2{x^4} - 3x - {x^3}} \right)} dx + \int_0^{2.5669} {\left( {{x^3} - {x^5} + 2{x^4} + 3x} \right)dx} \cr
& {\text{Integrating by using a CAS, we obtain}} \cr
& A \approx 1.121932 + 17.63719 \cr
& A \approx 18.759122 \cr} $$
