Question

For this Calculus question I keep getting 2/3 or 1/4. Where am I going wrong? Screenshot in the comments

Answer 1

The area of the shaded region is given by
\[\int_{-1}^1|y-y^3|~dy\]
or, if you take advantage of symmetry,
\[2\int_0^1(y-y^3)~dy\]