How to find the original function from a definite integral. I have that $\int_{0}^{x} f(x) \,dx = 2x,$ and I would like to find $f(x)$.
I am not even sure how to begin.
I would appreciate any help!

Note that the derivative of $\int_0^x g(t)dt$ is $g(x)$ whenever $g$ is continuous (See Fundamental theorem of calculus as mentioned by David). To get $g(\tilde x)$ you can calculate $\frac{d}{dx}\left.\int_0^x g(t)dt\right|_{x=\tilde x}$ ... 
