# Math Help - Integral practice

1. ## Integral practice

Given:
$\int _1^{x}f(t)dt = x^2 - 2x +1$

Find $f(x)$

2. Originally Posted by penguinpwn
Given:
$\int _1^{x}f(t)dt = x^2 - 2x +1$

Find $f(x)$
... take the derivative of both sides of the equation w/r to x

3. So would that lead to

$\int _1^{x}f(t)dt = x^2 - 2x +1$

$\frac {dt} {dx} = (2x - 2)dx$

Then what?

4. Originally Posted by penguinpwn

$\int _1^{x}f(t)dt = x^2 - 2x +1$

$\frac {dt} {dx} = (2x - 2)dx$

Then what?
are you not familiar with the Fundamental Theorem of Calculus? ...

$\frac{d}{dx} \int_a^x f(t) \, dt = f(x)$

5. I'm relatively new to the subject, but yes.

I just don't understand how it's applied here

6. $\frac{d}{dx} \left(\int _1^{x}f(t) \, dt = x^2 - 2x +1\right)$

$f(x) = 2x-2$

that's all there is to it.