theorem Th48: :: INTEGR19:48

for n being Element of NAT
for a, b, c, d being Real
for f being PartFunc of REAL,(REAL-NS n)
for g being PartFunc of REAL,(REAL n) st f = g & a <= b & ['a,b'] c= dom f & f | ['a,b'] is bounded & f is_integrable_on ['a,b'] & c in ['a,b'] & d in ['a,b'] holds
integral (f,c,d) = integral (g,c,d)