Answer
a. $F(x)=\sec x-2$
b. $F'(x)=\sec x\tan x$
Work Step by Step
a. See table on p.246.
$F(x)=\displaystyle \int_{\pi/3}^{x}\sec t\tan tdt=[\sec t]_{\pi/3}^{x}$
$=\displaystyle \sec x-\sec\frac{\pi}{3}$
$=\sec x-2$
b.
$\displaystyle \frac{d}{dx}[\sec x-2]=\sec x\tan x-0=\sec x\tan x$
