Suppose $f(x)\in C^1([0,1])$ and $f(0)=0$. Let
$\phi(x)= \begin{cases} \int_0^x\frac{f(t)}{\sqrt{x-t}}dt &\quad\text{if}\quad x\in(0,1]\\ 0&\quad\text{if}\quad x=0 \end{cases} $
(a) Prove that $\phi(x)\in C^1([0,1])$ and $ \phi'(x)=\int_0^x\frac{f'(t)}{\sqrt{x-t}}dt $
(b) Prove that $ f(x)=\frac1{\pi}\int_0^x\frac{\phi'(t)}{\sqrt{x-t}}dt $