theorem :: INTEGRA9:62

for n being Element of NAT
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 A c= Z & ( for x being Real st x in Z holds
x > 0 ) & dom (ln * (#Z n)) = Z & dom (ln * (#Z n)) = dom f2 & ( for x being Real st x in Z holds
f2 . x = n / x ) & f2 | A is continuous holds
integral (f2,A) = ((ln * (#Z n)) . (upper_bound A)) - ((ln * (#Z n)) . (lower_bound A))