theorem :: INTEGR12:3

for A being non empty closed_interval Subset of REAL
for f, f1 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
( exp_R . x < 1 & f1 . x = 1 ) ) & Z c= dom (arctan * exp_R) & Z = dom f & f = exp_R / (f1 + (exp_R ^2)) holds
integral (f,A) = ((arctan * exp_R) . (upper_bound A)) - ((arctan * exp_R) . (lower_bound A))