Thank you but I think I have it. Basically, you rewrite your integral.
if then write . Thus, we have,
By the subdivision rule,
(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