inf f(x) = x^2 + 5x - 3 then find the area between f(x) , x=1 and x=2

f(x) = x^2 + 5x - 3

Let F(x)
= integral f(x)

Then the area between f , x=1 and x= 2
is:

A = F(2) - F(1)

Then , let
us determine F(x) first.

F(x) = intg
f(x)

        = intg (x^2 + 5x -3)
dx

         = intg x^2 dx  + intg 5x dx  - intg 3
dx

         = x^3/3 + 5x^2 /2  -
3x

F(2) = 8/3 + 20/2 -
6

         = ( 16 + 60 - 36)/6 = 40/6 =
20/3

==> F(2) =
20/3

==> F(1) = 1/3 + 5/2 - 3 = (2 + 15 - 18)/6 = 
-1/6

==> A = F(2) - F(1) = 20/3 - -1/6 =
41/6

Then the area = 41/6 square
units.