theorem :: INTEGR14:28

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 & ( for x being Real st x in Z holds
f . x = ((exp_R . x) / (cos . x)) + (((exp_R . x) * (sin . x)) / ((cos . x) ^2)) ) & Z c= dom (exp_R (#) sec) & Z = dom f & f | A is continuous holds
integral (f,A) = ((exp_R (#) sec) . (upper_bound A)) - ((exp_R (#) sec) . (lower_bound A))