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## Main Question or Discussion Point

Hi, this has been bugging me for a long time: I am lacking a philosophical concept or just a general motivation behind the concept of an integral. To me, "computing the area under a graph" seems too specialized to me, especially how our pictorial representation of a function could have been arbitrary. When I ask why I should care about the integral at all, I'm usually given answers like "to find the volume of a swimming pool.." , " to build MRI scans.." and I am unsatisfied with these answers. When I study algebra (vector spaces, rings ) it has a nice "beautiful picture" behind it.. I do not find this same intrinsic interest when I look at integration, can someone help motivate or enlighten me? thank you