I’m studying the following function $$f(t)=\int_0^t (t-s)^{-\frac{3}{4}}s^{-\frac{1}{4}}ds.$$ It is clear that $f(t) >0$ for $t\in (0,1],$ since $-\frac{3}{4}>-1$ and $-\frac{1}{4}>-1$.
I want to know if there exists $C>0$ such that for all $t \in (0,1],$ $$f(t) \le C.$$
Also, I’d like to know if $\lim_{t\to 0^+} f(t)$ exists.
I would be appreciate it if you give any comments for my questions.