Find the maximum and minimum of the following integral in terms of $f(x),a,C$:
\begin{align}I=\int_{0}^{a} \frac{x}{f(x)}p(x)dx \end{align}
s.t.:
1) $\int_{0}^{a} p(x)dx=1$
2) $\int_{0}^{a} f(x)p(x)dx=C$
Notes:
1) $p(x)$ is an unknown probability density function.
2) $x,f(x),p(x)\geq 0 \;,\; C>0$
3) $f(0)=0$
4) $\lim_{x \to 0}\frac{x}{f(x)}=0$