theorem :: INTEGR12:6

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)) - (exp_R / (sin ^2)) holds
integral (f,A) = ((exp_R (#) cot) . (upper_bound A)) - ((exp_R (#) cot) . (lower_bound A))