How to find the integral of f(x) =x^3 - 5 between [ 1, 2]

Given the curve f(x) = x^3 -
5

We need to find the definite integral on the interval [1,
2].

Let us intergrate
f(x).

Let F(x) = intg
f(x)

==> The defininte integral is
:

 I = F(2) - F(1).

==>
F(x) = intg (x^3 - 5) dx

              = intg x^3 dx - intg
5 dx

               = x^4/4 - 5x +
C

==> F(2) = 2^4/4 - 5*2  +
C

              = 4 - 10 + c = -6 +
c

==> F(1) = 1/4 - 5 + C = -19/4 +
C

==> I = -6 + 19/4 = ( -24 + 19) /4 =
-5/4

==> Then, the integral is I =
-5/4