Let $\{f_n\}_n$ be a sequence of real-valued continuous functions defined on $[0,1]$ such that $\int^1_0|f_n(y)|dy\leq3$ for all $n$. Define $g_n:[0,1]\rightarrow\mathbb{R}$ by
$g_n(x)=\int^1_0\sqrt{x+y}f_n(y)dy$
I have to prove that $\{g_n\}_n$ contains a subsequence that converges uniformly on $[0,1]$.
I really don't know where to start, could you help me please?