theorem :: INTEGR13:32

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 * exp_R) ^2) & Z c= dom (cot * exp_R) & Z = dom f & f | A is continuous holds
integral (f,A) = ((- (cot * exp_R)) . (upper_bound A)) - ((- (cot * exp_R)) . (lower_bound A))