Find the area between the parabola f(x) = x^2 - 3x +5 and the lines x= 0 and x = 2.

First, the area which has to be calculated is located
between the given curve f(x), the lines x = 0 and x = 2, also the x
axis.

To calculate the area, we'll use the
formula:

S = Integral (f(x) - ox)dx = Int f(x)dx = Int (x^2
- 3x +5)dx

Int (x^2 - 3x +5)dx = Int x^2dx - 3Int xdx +
5Int dx

Int x^2dx = x^3/3 +
C

Int x dx = x^2/2 + C

Int dx
= x + C

Int x^2dx - 3Int xdx + 5Int dx = x^3/3 -3x^2/2 + 5x
+ C 

Now, we'll calculate the value of the area, using
Leibnitz Newton formula::

S = F(2) - F(0),
where

F(2) = 2^3/3 -3*2^2/2 + 5*2 = 8/3 - 12/2 + 10 = 8/3 +
4 = 20/3

F(0) = 0^3/3 -3*0^2/2 + 5*0 =
0

S = 20/3 - 0

S
= 20/3