you subtracted the functions incorrectly
top function - bottom function
Now I know I'd set them equal to each other to find the points of intersection in other words the bounds of the integral and it'd come out to be 0 and 1. The integral would then be from 0 to 1 of 4x^2-(7x-3x^2) which would give me 7x^2-7x and I get a negative answer. I know this can't be correct since you can't have negative area but what am I doing wrong?