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

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

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

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

Thanks.