Answer
$$\tan t$$
Work Step by Step
$$\eqalign{
& f\left( t \right) = {\sec ^2}t \cr
& {\text{find an antiderivative of }}f\left( t \right) \cr
& F\left( t \right) = \tan t + C \cr
& {\text{using the initial condition }}F\left( {\pi /4} \right) = 1 \cr
& 1 = \tan \left( {\frac{\pi }{4}} \right) + C \cr
& 1 = 1 + C \cr
& {\text{then}} \cr
& C = 0 \cr
& {\text{so}}{\text{,}} \cr
& = \tan t + 0 \cr
& = \tan t \cr} $$