theorem :: INTEGR11:64

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
f . x = ((cos . x) - ((sin . x) ^2)) / ((sin . x) ^2) ) & Z c= dom ((- cosec) - (id Z)) & Z = dom f & f | A is continuous holds
integral (f,A) = (((- cosec) - (id Z)) . (upper_bound A)) - (((- cosec) - (id Z)) . (lower_bound A))