Вычислите опроделёный интеграл

∫[1;-2] (x^2-2x+4)dx

∫[1;-2] (x^2-2x+4)dx = [x^3/3 - x^2 + 4x] from x=1 to x=-2

Plugging in the limits of integration, we get:

(-2)^3/3 - (-2)^2 + 4(-2) - (1)^3/3 + (1)^2 + 4(1) = -8/3 - 2 - 8 - 1/3 + 1 + 4

Simplifying, we get:

-11 2/3

Therefore, the definite integral ∫[1;-2] (x^2-2x+4)dx is equal to -11 2/3.