# Indefinite Integrals Without Differentation and Fundamental Theorem

As you know we can solve definite integrals using the definition over limit (without using antiderivatives at all). So I what I ask is how to solve an indefinite integral like that? For example $$\int x^2 \, dx$$ , we all know the result is x^3/3 + c. But we got this by using differentation and Fundamental Theorem of Calculus. How can we calculate this without using them?

• Indefinite integrals are by definition anti-derivatives. There is no direct limit definition for them. – Paramanand Singh Jan 6 '19 at 16:43

Divide the interval into n parts and use $$\sum_{k=1}^n k^2 =n(n+1)(2n+1)/6 =n^3/3+$$ smaller terms.