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In the appendix to ONAG (2nd edition), Conway points that the definition of integration (using Riemann sums as left and right options) gives the "wrong" answer : $\int_0^\omega \exp(t)\thinspace dt=\exp(\omega)$ (instead of $\exp(\omega)-1$). I wonder if this was not due to lack of some options (presumably right ones), and if a better definition could not be sought by using Kurzweil-Handstock integration (but I was not able to concoct one, of course, else I would not ask here). Has the idea already been tried?

In the appendix to ONAG (2nd edition), Conway points that the definition of integration (using Riemann sums as left and right options) gives the "wrong" answer : $\int_0^\omega \exp(t)\thinspace dt=\exp(\omega)$ (instead of $\exp(\omega)-1$). I wonder if this was not due to lack of some options (presumably right ones), and if a better definition could not be sought by using Kurzweil-Henstock integration (but I was not able to concoct one, of course, else I would not ask here). Has the idea already been tried?

In the appendix to ONAG (2nd edition), Conway points that the definition of integration (using Riemann sums as left and right options) gives the "wrong" answer : $\int_0^\omega \exp(t)\thinspace dt=\exp(\omega)$ (instead of $\exp(\omega)-1$). I wondered if this was not due to lack of some options (presumably right ones), and if a better definition could not be seeked by using Kurzweil-Handstock integration (but I was not able to concoct one, of course, else I would not ask here). Has the idea already been tried?

In the appendix to ONAG (2nd edition), Conway points that the definition of integration (using Riemann sums as left and right options) gives the "wrong" answer : $\int_0^\omega \exp(t)\thinspace dt=\exp(\omega)$ (instead of $\exp(\omega)-1$). I wonder if this was not due to lack of some options (presumably right ones), and if a better definition could not be sought by using Kurzweil-Handstock integration (but I was not able to concoct one, of course, else I would not ask here). Has the idea already been tried?