theorem :: INTEGR12:10

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 & Z = dom f & f = (exp_R * cos) (#) sin holds
integral (f,A) = ((- (exp_R * cos)) . (upper_bound A)) - ((- (exp_R * cos)) . (lower_bound A))