theorem :: INTEGR11:60

for A being non empty closed_interval Subset of REAL
for Z being open Subset of REAL
for f being PartFunc of REAL,REAL st A c= Z & ( for x being Real st x in Z holds
( sin . x > 0 & f . x = (cot . x) ^2 ) ) & Z c= dom ((- cot) - (id Z)) & Z = dom f & f | A is continuous holds
integral (f,A) = (((- cot) - (id Z)) . (upper_bound A)) - (((- cot) - (id Z)) . (lower_bound A))