I know this is a very simple question, and I have searched it too. How to avoid incorrect symbols in calculation results.I don’t understand how to choose the sign of $ds$.

An object moves from a to b,Note the number $b<a$.

[![enter image description here][1]][1]
Take the direction of $i$ as the positive direction,Can I think of $\vec{ds}$ as $\vec{b}-\vec{a}$?

$\int _{a}^{b} {-F}-{ds}=W<0$

I know that the choice of ab determines the positive and negative, maybe I should write $\int _{a}^{b} {-F}{ds}=w>0$

BUT
[![enter image description here][2]][2]
I changed the direction of i

Write  the formula $\int _{a}^{b} {F}{ds}=W<0$

How do I decide the sign of $ds$?Do I made any errors about the vector of ab and ds?



  [1]: https://i.sstatic.net/GD2sY.png
  [2]: https://i.sstatic.net/kLul1.png