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    $\begingroup$ I thought of this, but the integration limits are represented abstractly, as "initial" to "final", and given that abstract representation it's not necessary to swap them to go from final to initial. I mean, to be a bit more precise with the notation, the question has something like $\int_{s_i}^{s_f} (\cdots)\mathrm{d}s \to \int_{y_i}^{y_f} (\cdots)\mathrm{d}y$. $\endgroup$ Commented Nov 29, 2018 at 8:31
  • $\begingroup$ Even if there are Abstract Limits, These are changed, when you swap the sign $\endgroup$ Commented Nov 29, 2018 at 8:32
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    $\begingroup$ I don't think so... when you change variables, if you were integrating from the initial to the final value of the original variable, you integrate from the initial to final value of the new variable, without any extra sign change regardless of what the change of variables is. For example defining $z = -y$, $y_i = 0$ and $y_f = 1$, we have $\int_{y_i}^{y_f} \mathrm{d}y = y_f - y_i = 1$ and $\int_{y_i}^{y_f} \mathrm{d}y = \int_{z_i}^{z_f} \frac{\mathrm{d}z}{\mathrm{d}y} \mathrm{d}z = \int_{z_i}^{z_f} (-1) \mathrm{d}z = (-1)(z_f - z_i) = -(-1 - 0) = 1$. $\endgroup$ Commented Nov 29, 2018 at 8:46
  • $\begingroup$ @DavidZ I think kyromaxim it's saying what you are saying. You make the limits negative. I don't think they are saying to swap initial with final and vice versa. $\endgroup$ Commented Nov 29, 2018 at 11:51