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!