Answer
$$1$$
Work Step by Step
$$\eqalign{
& \int_0^{\pi /3} {\sec x\tan x} dx \cr
& {\text{integrate using the basic rules for integration}} \cr
& = \left. {\left( {\sec x} \right)} \right|_0^{\pi /3} \cr
& {\text{using the fundamental theorem}} \cr
& = \sec \left( {\frac{\pi }{3}} \right) - \sec \left( 0 \right) \cr
& {\text{Simplify}} \cr
& = 2 - 1 \cr
& = 1 \cr} $$