theorem :: INTEGR13:4

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 = 2 (#) (exp_R (#) cos) & Z c= dom (exp_R (#) (sin + cos)) & Z = dom f & f | A is continuous holds
integral (f,A) = ((exp_R (#) (sin + cos)) . (upper_bound A)) - ((exp_R (#) (sin + cos)) . (lower_bound A))