why is an anti-derivative needed for integration
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The anti-derivative isn’t necessarily *needed* for integration. You could theoretically solve an integral by summing up the area under the curve through brute-force methods like Riemann sums.
However, the entire point of calculus is that derivatives and integrals are the opposite of each other. It’s such a key point that it’s literally named the “Fundamental Theorem of Calculus”.
So if you can do a derivative, and you can figure out how to do it backwards, then you can do an integral. It’s not that it’s *needed*, it’s that it’s a way easier method than trying to brute-force it.
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