Find the function f(x) when the equation of the derivative of f(x) is given.

Question

This is what is given: $f '(x)=y=4x-5$

Find: the function, $f(x)$, of which $f '(x)$ is the derivative of.

Answer 1

In general:

$$\int \:\frac{d}{dx}\left(f\left(x\right)\right)dx=F\left(x\right)+constnat$$

In your case:

$\int \:\left(4x-5\right)dx=F\left(x\right)+constant$

Can you find $F(x)$?

Answer 2

your $f(x)= 2x^2-5x +C$ is unique up to a constant $C$.