Then ∫
( )
b
a f x dx = [F( )] =
ab
x
 F (b) – F(a) Remarks
(i)
In words, the Theorem 2 tells us that 
( )
b
∫a f x dx
= (value of the anti derivative F
of f at the upper limit b – value of the same anti derivative at the lower limit a) (ii)
This theorem is very useful, because it gives us a method of calculating the
definite integral more easily, without calculating the limit of a sum (iii)
The crucial operation in evaluating a definite integral is that of finding a function
whose derivative is equal to the integrand