theorem Th13: :: INTEGR18:13

for X being RealNormSpace
for r being Real
for A being non empty closed_interval Subset of REAL
for f being PartFunc of REAL, the carrier of X st A c= dom f & f is_integrable_on A holds
( r (#) f is_integrable_on A & integral ((r (#) f),A) = r * (integral (f,A)) )