Thank you but I think I have it. Basically, you rewrite your integral.
The integral,
if then write . Thus, we have,
By the subdivision rule,
But,
(Same when )
And the proof it complete.
If is a countinous real function, we define,
as being convergent if there exists a such as, and are convergent. Also its value is then,
.
Prove that if,
is convergent then for any the two improper integrals,
are also convergent.
Further, prove that,
.
Thus, proving that the value of
is well-defined.
???