theorem :: INTEGR26:40

for a, b being Real
for f being PartFunc of REAL,REAL st a < b & [.a,b.] c= dom f & f | [.a,b.] is continuous holds
ex F being PartFunc of REAL,REAL st
( F is_antiderivative_of f,['a,b'] & ( for x being Real st x in [.a,b.] holds
F . x = integral (f,a,x) ) )