Calculus: Difficult Integration

Question on @Quora:

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In our 1978 French Classes Préparatoires aux Grandes Ecoles 1st year “Mathématiques Supérieures”,  we wanted to ‘test’ our admired Math Professor whom we think was a “super know-all” mathematician. We asked him the above question. He immediately scolded us in the unique French mathematics rigor:

“L’intégration n’a pas de sense!
Quelle-est la domaine de définition?”

(The integration has no meaning! What is the domain of definition ?)

He was right!

Under the Singapore – British GCE Math education, we lack the rigor of mathematics. We are skillful in applying many tricks to integrate whatever functions, but it is meaningless without specifying the domain (interval) in which the function is defined ! Bear in mind Integration of a function f (curve) is to calculate the Area under the curve f within an interval (or Domain, D). If f is not defined in D, then it is meaningless to integrate f because there won’t be any Area.

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