Eli5 how do we know that the integration of x^n is x^(n+1)/n+1

Question

Eli5 how do we know that the integration of x^n is x^(n+1)/n+1

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Answer 1

A small note, this pattern was discovered before calculus was invented. Several people independently discovered it although they couldn’t make a rigorous proof they started using it for positive whole number powers.