(1)
( )
c
∫a f x dx
 = F(c) – F(a) (2)
and
( )
b
∫c f x dx
 = F(b) – F(c) (3)
342
MATHEMATICS
Adding (2) and (3), we get 
( )
( )
F( ) – F( )
( )
c
b
b
a
c
a
f x dx
f x dx
b
a
f x dx
+
=
=
∫
∫
∫
This proves the property P2 Proof of P3  Let t = a + b – x