theorem :: INTEGR13:35

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 / ((x ^2) * ((cos . (1 / x)) ^2)) ) & Z c= dom (tan * ((id Z) ^)) & Z = dom f & f | A is continuous holds
integral (f,A) = ((- (tan * ((id Z) ^))) . (upper_bound A)) - ((- (tan * ((id Z) ^))) . (lower_bound A))