Answer
See explanation.
Work Step by Step
(a)
\[
\frac{d}{d x} \int_{1}^{x} \sin \left(t^{2}\right) d t=\sin \left(x^{2}\right)
\]
$(\mathbf{b})$
$\frac{d}{d x} \int_{1}^{x} \sqrt{1-cos\ t} \ dt \\ =\sqrt{1-cosx}$
Remember :
\[
\frac{d}{d x} \int_{a}^{x} f(t) d t=f(x)
\]