theorem Th37: :: INTEGR26:37

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