theorem Th44: :: INTEGR19:44

for n being Element of NAT
for A being non empty closed_interval Subset of REAL
for f being PartFunc of REAL,(REAL n)
for g being PartFunc of REAL,(REAL-NS n) st f = g & f | A is bounded & A c= dom f & f is_integrable_on A holds
( g is_integrable_on A & integral (f,A) = integral (g,A) )