# Calculate the integral of (x^3-4x^2+1) from 1 to 2 using the fundamental theorem of calculus.

Fundamental theorem of calculus says:

Let `f` be continous real-valued function defined on segment `[a,b]` and let `F` be defined as

`F=int_a^x f(t)dt.`

Then `F` is continous and differentiable on `(a,b)` and for all `x in (a,b)`

`F'(x)=f(x)`

For calculating definite integral we usually use corollary of this theorem, also known as Newton-Leibniz formula

Same assumptions as in previous theorem and

`int_a^bf(x)dx=F(b)-F(a)`

This is sometimes called second fundamental theorem of calculus.