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## Main Question or Discussion Point

Hello,

I was just wondering, we have what could be called the indefinite derivative in the form of d/dx x^2=2x & evaluating at a particular x to get the definite derivative at that x. But with derivation, we can algebraically manipulate the limit definition of a derivative to actually evaluate to 2x from x^2. Is there a similar process available to algebraically manipulate a limit definition of an indefinite integral to get the expected result?

Integration is normally just taught as the reverse of derivation, and while that works of course, I was just curious if there was a way to directly determine the indefinite integral of a function by using limits or differentials.

I was just wondering, we have what could be called the indefinite derivative in the form of d/dx x^2=2x & evaluating at a particular x to get the definite derivative at that x. But with derivation, we can algebraically manipulate the limit definition of a derivative to actually evaluate to 2x from x^2. Is there a similar process available to algebraically manipulate a limit definition of an indefinite integral to get the expected result?

Integration is normally just taught as the reverse of derivation, and while that works of course, I was just curious if there was a way to directly determine the indefinite integral of a function by using limits or differentials.