theorem :: INTEGRA8:60

for f2 being PartFunc of REAL,REAL
for A being non empty closed_interval Subset of REAL
for Z being open Subset of REAL st A c= Z & dom cot = Z & dom cot = dom f2 & ( for x being Real st x in Z holds
( f2 . x = - (1 / ((sin . x) ^2)) & sin . x <> 0 ) ) & f2 | A is continuous holds
integral (f2,A) = (cot . (upper_bound A)) - (cot . (lower_bound A))