# If you knew the definite integral between every point of a function, could you compute its indefinite integral?

So for a function like 2x, if you knew the definite integral from every point 0 to 1, 1 to 2, 2 to 3, etc... Is there an algorithm/equation that could find its indefinite integral of x^2+c? If so how many definite integrals are needed to compute the indefinite function accurately?

• Yes, it's the function $x\mapsto \int_{a_0}^xf(t)\,dt$. Varying the starting point $a_0$ of the integral (basically) corresponds to the constant $+c$ of the indefinite integral. But we need continuum many (but at least countably infinite) values. – Berci Mar 14 at 23:08
• Berci, thanks for the response. I don't really understand that as I am just in Calc 2 and not great at this stuff but I will ask my professor if he could expand on it. Thanks again. – Brian Mar 14 at 23:51
• The differential of the integral function $F:x\mapsto \int_{a_0}^xf$ at point $x$ is just $f(x)$. – Berci Mar 15 at 0:25