theorem :: INTEGR11:45

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 & Z c= ].(- 1),1.[ & ( for x being Real st x in Z holds
f . x = 1 / (1 + (x ^2)) ) & Z = dom f & f | A is continuous holds
integral (f,A) = (arctan . (upper_bound A)) - (arctan . (lower_bound A))