Can someone please help me with integrals

Find:

∫ f(x) dx from x = 0 to x = 4 if f(x) =

2, for x < 2
X, for x ≥ 2

Break the integral up

int(f(x) * dx , x = 0 , x = 2) + int(f(x) * dx , x = 2 , x = 4)

First, we can see that f(x) is continuous along this interval, and that's important

int(2 * dx , x = 0 , x = 2) + int(x * dx , x = 2 , x = 4) =>
2x {0 , 2} + (1/2) * x^2 {2 , 4} =>
2 * (2 - 0) + (1/2) * (4^2 - 2^2) =>
2 * 2 + (1/2) * (16 - 4) =>
4 + (1/2) * 12 =>
4 + 6 =>
10