Answer
$A = \int_{ - 1}^1 {\left( {2 - {y^2} - {y^4}} \right)} dy$
Work Step by Step
$$\eqalign{
& {\text{Let the functions }}x = {y^4}{\text{ and }}x = 2 - {y^2} \cr
& {\text{Graph the curves using Geogebra }}\left( {{\text{Shown Below}}} \right) \cr
& \cr
& {\text{We can find the area integrating with respect to }}y \cr
& A = \int_c^d {\left[ {f\left( y \right) - g\left( y \right)} \right]} dy{\text{ }}\left( {\bf{1}} \right){\text{ }} \cr
& x = 2 - {y^2} \geqslant x = {y^4}{\text{ into the interval }}\left[ { - 1,1} \right],{\text{ then}} \cr
& {\text{Let }}f\left( y \right) = 2 - {y^2}{\text{ and }}g\left( y \right) = {y^4},{\text{ }}\underbrace {\left[ { - 1,1} \right]}_{\left[ {c,d} \right]} \cr
& {\text{Substituting into }}\left( {\bf{1}} \right){\text{ we obtain}} \cr
& A = \int_{ - 1}^1 {\left[ {\left( {2 - {y^2}} \right) - \left( {{y^4}} \right)} \right]} dy \cr
& A = \int_{ - 1}^1 {\left( {2 - {y^2} - {y^4}} \right)} dy \cr} $$
