theorem :: INTEGR12:8

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
f1 . x = 1 ) & Z c= ].(- 1),1.[ & Z = dom f & f = (exp_R (#) arccot) - (exp_R / (f1 + (#Z 2))) holds
integral (f,A) = ((exp_R (#) arccot) . (upper_bound A)) - ((exp_R (#) arccot) . (lower_bound A))