Find the area between the curve f(x) = 3x^2 - 2x +1 and x=0 and x= 1

To compute the area between the given curve and lines,
we'll apply Leibniz Newton formula:

Int f(x) dx = F(a) -
F(b)

First, we'll compute the indefinite integral of
f(x):

Int (3x^2 - 2x
+1)dx

We'll apply the property of integral to be additive
and we'll get:

Int (3x^2 - 2x +1)dx = Int 3x^2dx - 2Int xdx
+ Int dx

Int (3x^2 - 2x +1)dx = 3*x^3/3 - 2*x^2/2 +
x

We'll simplify and we'll
get:

Int (3x^2 - 2x +1)dx = x^3 - x^2 +
x

We'll apply Leibniz Newton formula for b = 1 and a =
0.

F(b) = F(1) = 1 - 1 + 1 =
1

F(a) = F(0) = 0 - 0 + 0 =
0

Int (3x^2 - 2x +1)dx = F(1) -
F(0)

Int (3x^2 - 2x +1)dx = 1 -
0

Int (3x^2 - 2x +1)dx =
1

The area located under the curve and
between the line is A = 1 square unit.