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correct me if I'm wrong but "y" is a variable, the d is supposed to represent a differential amount of "y" because that is an integral and usually they tell you what variable you integrate with respect to. In fact I believe that equation is a convolution between the function f and g which is essentially the operation you perform when applying a blurring function. That brings me to a question myself that is, why is the dy raised to the power of 2?