y x2 6x 9 2

Solution

y=x^2-6x+9 y=(x-3)^2 .\'.Area under the curve(total area of the region between the curve and the x-axis) = ?(x=2 to x=4) (x-3)^2 dx = ?(x=2 to x=4) (x-3)^2 d(x-3) = [(x-3)^3/3](x=2 to x=4) = (4-3)^3 / 3 - (2-3)^3 / 3 = 1/3 - (-1/3) = 2/3 sq units.