<s>[INST] Find $f'(1)$ given $f(x)$ and $f(1)$ Question:

Let $$f(x)=\int\frac{x-1}{x+1}\frac{dx}{\sqrt{x^3+x^2+x}}$$ such that $f(1)=\frac{2\pi}{3}$
Then $f'(1)$ is equal to
A) $0$
B) $\cfrac \pi3$
C) $\cfrac\pi4$
D) $2$

Attempt:

\begin{align}f(x)&=\int\frac{x-1}{x+1}\frac{1}{\sqrt{x^3+x^2+x}}dx\\
f(1)&=\int0dx\\
f(1)&=0+c\\
&= \frac{2\pi}{3}\\
\implies c&= \frac{2\pi}{3}
\end{align}

I don't know what to do beyond this step. This is an indefinite integral so we cannot differentiate it. How else we bring $f'(x)$ into picture? Any hints?
 [/INST] Does $f'(x)$ mean $\frac{df}{dx}$. Isnt $f'(x)$ then simply the integrated term, with the integration removed? ie, $\frac{x-1}{x+1}\times \frac{1}{\sqrt{x + x^2 + x^3}}$ ?  Am I missing something?
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