theorem Th6: :: INTEGR19:6

for a, b, c, d, r being Real
for f being PartFunc of REAL,REAL st a <= c & c <= d & d <= b & f is_integrable_on ['a,b'] & f | ['a,b'] is bounded & ['a,b'] c= dom f holds
( r (#) f is_integrable_on ['c,d'] & (r (#) f) | ['c,d'] is bounded )