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

The *antiderivative* of x^n is any function x^(n+1)/(n+1)+c, because the derivative of x^(n+1)/(n+1)+c is x^n.

The reason the derivative of x^(n+1)/(n+1)+c is x^n is [binomial theorem](https://en.wikipedia.org/wiki/Power_rule#Proof_by_binomial_theorem_(natural_numbers)).