Find the area between the curves
y=(x^3)-10(x^2)+24x and y=(-x^3)+10(x^2)-24x
First find the points where the curves intersect. One of the points is x=0. There are two other points, 4 and 6.
Between one pair of points, y1>y2
Between the two other points, y2>y1.
Then integrate the absolute value of the difference between the two function, between the x-values where they intersect. You may have to do the integral twice, changing the sign of the integrand