theorem :: INTEGRA6:25

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