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 $b<a$.

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 I changed the direction of i

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

I can judge the positive or negative of the result by the order of the upper and lower limits of the integral and the sign of F. If it does not match, I will take the opposite sign for ds.I don’t want to judge and correct by the prediction result.

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