Simple or double integration?

If I want to compute the area of the region bounded by the graphs y=x and y=x^2-2x, can I simply compute the integral of (x-(x^2-2x)) dx from x=0 to x=3, or do I have to use double integration?

In any case, why?

For two curves, f(x) and g(x) the area of the element between x and x+dx is simply |f(x)-g(x)|dx. The magnitude sign is there only if you don't want the area to go negative when the curves cross.

So the total area = Int |f(x)-g(x)|dx

"Ordinary" integration will do.

HallsofIvy
$$\int_0^3 (x- (x^2- 2x))dx= \int_0^3 (3x- x^2)dx$$
$$\int_{x=0}^3 \int_{y= x^2- 2x}^x dy dx$$