What is the proof that an area under a curve is the definite

Approximating Area

In order to find the area between two functions, should the definite integrals of both functions be equal to a positive value for that space? - Quora

How does the area of an infinite rectangle under the curve become simple definite integral formulae? - Quora

How does the area of an infinite rectangle under the curve become simple definite integral formulae? - Quora

Solved Use a definite integral to find the area under the

AS Maths - Proof that integration relates to finding areas

What is the proof for the property, 'Two indefinite integrals with the same derivative lead to the same family of curves and so they are equivalent'? - Quora

Area Under The Curve - Method, Formula, Solved Examples, FAQs

Area Under The Curve - Method, Formula, Solved Examples, FAQs

Calculus: Why does integrating a function give area under its curve?

Ex 2: Find the Area Under a Curve Using a Geometric Formula

AS Maths - Proof that integration relates to finding areas

In order to find the area between two functions, should the definite integrals of both functions be equal to a positive value for that space? - Quora

Methods to determine area under curve

Area as Definite Integral - GeeksforGeeks