A=22/10
A=integral(a,b) [f(x)-g(x)]dx
Since the function is even (the function is mirrored over the y axis) we can evaluate the integral from 0 to 1 and then multiply our answer by 2 since we have the same area on each side of the y axis.
We get A=2*int.(0, 1)[(x^2)-(-2x^4)]dx
Now we can integrate by term.
2*[int.(0, 1)[x^2]dx+int(0, 1)[2x^4]dx]
Now factor out constants.
2*[int(0,1)[x^2]dx+2int(0,1)[x^4]dx]
Now integrate.
2*[(x^3/3)|(0,1) + 2*(x^5/5)|(0,1)]
Now solve.
2*[(1/3)+2*(1/5)]
=22/10
Hope you can decipher what I wrote!