theorem :: INTEGRA9:63

for A being non empty closed_interval Subset of REAL
for f2 being PartFunc of REAL,REAL
for Z being open Subset of REAL st not 0 in Z & A c= Z & dom (ln * ((id Z) ^)) = Z & dom (ln * ((id Z) ^)) = dom f2 & ( for x being Real st x in Z holds
f2 . x = - (1 / x) ) & f2 | A is continuous holds
integral (f2,A) = ((ln * ((id Z) ^)) . (upper_bound A)) - ((ln * ((id Z) ^)) . (lower_bound A))