theorem Th35: :: INTEGR26:35

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_right_differentiable_in a & Rdiff (F,a) = lim_right ((F `| ].a,b.[),a) )