This strengthens the relationship
between differentiation and integration (iv)
In 
( )
b
∫a f x dx
, the function f needs to be well defined and continuous in [a, b] For instance, the consideration of definite integral 
1
3
2
2
2 (
x x–1)
dx
−∫
 is erroneous
since the function f expressed by f(x) = 
1
2
2
(
x x–1)
 is not defined in a portion
– 1 < x < 1 of the closed interval [– 2, 3] 336
MATHEMATICS
Steps for calculating 
( )
b
∫a f x dx