Find the area bounded between the curve f(x) = 3x^2-4x +2 and the line y= 2x-1

First let us determine the points of intersection of the curve
f(x) = 3x^2- 4x +2 and the line y= 2x-1.

2x - 1 = 3x^2 - 4x +
2

=> 3x^2 - 6x + 3 = 0

=>
x^2 - 2x + 1 = 0

=> (x -1)^2 =
0

=> x = 1

The line is
tangential to the curve.

There is no area bounded
between the curve f(x) = 3x^2- 4x +2 and the line y= 2x-1.