theorem :: INTEGR13:11

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