Let this be F(x) There is no need to keep
integration constant C because if we consider F(x) + C instead of F(x), we get
( )
[F ( )
C]
[F( )
C]– [F( )
C]
F( ) – F( )
b
ab
a f x dx
x
b
a
b
a
=
+
=
+
+
=
∫ Thus, the arbitrary constant disappears in evaluating the value of the definite
integral (ii)
Evaluate F(b) – F(a) = [F ( )]b
xa
, which is the value of  
( )
b
∫a f x dx