theorem :: INTEGR12:14

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