Its not dangerous as long one knows what one is doing. This is a poster boy of an example to illustrate the concept that if you have a sequence of functions f_

Its not dangerous as long one knows what one is doing. This is a poster boy of an example to illustrate the concept that if you have a sequence of functions f_i that becomes indistinguishable to the eye (being vague on purpose) from some function f, it does not mean that integral of that sequence will be close to the integral of f -- mathematical rigor does not matter except when it does