Solution
= Solution
\b[Both functions are integrable on $(0,1)$.] The oscillatory function is measurable and bounded by $1$ in absolute value, on an <interval> of finite measure. For the other function,
$$
\int_0^1h(x)\,dx=\int_0^1\frac{dx}{\sqrt{1-x^2}}=\frac\pi2<\infty.
$$
In particular its singularity at the right endpoint is of integrable inverse-square-<root> type.