theorem :: INTEGR14:35

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 & ( for x being Real st x in Z holds
f . x = ((1 / (sin . x)) / (x ^2)) + (((cos . x) / x) / ((sin . x) ^2)) ) & Z c= dom (((id Z) ^) (#) cosec) & Z = dom f & f | A is continuous holds
integral (f,A) = ((- (((id Z) ^) (#) cosec)) . (upper_bound A)) - ((- (((id Z) ^) (#) cosec)) . (lower_bound A))