theorem :: INTEGR14:21

for A being non empty closed_interval Subset of REAL
for f being PartFunc of REAL,REAL
for Z being open Subset of REAL st A c= Z & f = (exp_R * sec) (#) (sin / (cos ^2)) & Z = dom f & f | A is continuous holds
integral (f,A) = ((exp_R * sec) . (upper_bound A)) - ((exp_R * sec) . (lower_bound A))