The area of interest is symmetrical about the origin, so can be found by doubling the integral for the area in the first quadrant. Then the total area is
[tex]A= 2\int\limits^{0.5}_{0}{(1-2x^2-x)} \, dx =2\left(0.5-\frac{2}{3}0.5^{3}-\frac{1}{2}0.5^2\right)\\A=1-\frac{1}{6}-\frac{1}{4}=1-\frac{5}{12}\\\\A=\dfrac{7}{12}[/tex]
