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

calculus - Why is the area under a curve the integral? - Mathematics Stack Exchange

What is the proof that an area under a curve is the definite integral of that function? - Quora

Calculus - Integration

AS Maths - Proof that integration relates to finding areas

Why is the definite integral the area under the curve? - Quora

What is the intuition for why integration is the area beneath a function? - Quora

Integration: The Area Under the Curve

3. Areas Under Curves

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