Newton-leibnitz formula:
This theorem state that If f(x) is the continuous function on [a, b] and F(x) is any anti derivative of f(x) on [a, b] i.e. 
(x) = f (x) ∀x ∈ (a, b), then a∫b Fxdx = F(b) - F(a)
The function F(x) is integral of f(x) and a and b are lower and the upper limits of integration.
Illustration: Evaluate 
directly as well as by substitution x = 1 /t. Examine as to why the answers do not tally?
Solution:
On other hand; if x = 1/t then,
In above 2 results l = - p/4 is wrong. Since the integrand 
and thus the definite integral of this function cannot be negative.
As x = 1/t is discontinuous at t = 0, the substitution is not valid (\ I = Π/4).
Note: It is significant the substitution should be continuous in the interval of integration.
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