Answer
See explanation.
Work Step by Step
(a) $F^{\prime}(x)=\cos 2 x$
(b) $F(x)=\int_{\pi / 4}^{x} \cos 2 t d t=\left(\frac{1}{2} \sin 2 t\right)_{\pi / 4}^{x}=-\frac{1}{2}+\frac{1}{2} \sin 2 x$
Differentiating then gives $F^{\prime}(x)=\cos 2 x$
