Calculate the area of the shape bounded by the lines y = x ^ 2-2, y = 2x-2

y = x ^ 2 – 2, y = 2x – 2.
Find the intersection points of the function graphs:
x ^ 2 – 2 = 2x – 2,
x ^ 2 – 2 – 2x + 2 = 0,
x ^ 2 – 2x = 0,
x * (x -2) = 0,
x = 0 or x – 2 = 0, x = 2.
S = integral from 0 to 2 (2x – 2 – (x ^ 2 – 2)) dx = integral from 0 to 2 (2x – x ^ 2) dx = (x ^ 2 – x ^ 3/3) I from 0 to 2 = (2 ^ 2 – 2 ^ 3/3) – (0 ^ 2 – 0 ^ 3/3) = 4 – 8/3 = 1 integer 1/3.
Answer: 1 whole 1/3.