Define a real function $\displaystyle h:[-1,1]\to R$ by:

$\displaystyle h(x)=\int_{-1}^x\frac{g(t)}{\sqrt{1-t^2}}dt$, where $\displaystyle h(-1)=h(1)=0$

$\displaystyle g\in C[-1,1]$, i.e., $\displaystyle g$ is continuous in [-1,1].

I would like to know if the function $\displaystyle h$ is Holder continuous in [-1,1].

Thanks.