(Solved): ( 65 points each, \( +5 \) points) You can do one additional page of the final to replace one of th ...

( 65 points each, \( +5 \) points) You can do one additional page of the final to replace one of these three pages. If you do, mark that page as Test 4 on the cover and the top of the page. 1. Let \( \vec{F}(x, y)=\langle y+1, x-1\rangle=(y+1) \vec{i}+(x-1) \vec{j} \) a. Show that \( F \) is conservative, and find a potential function for \( F \). b. Compute the line integral \( \int_{C} \vec{F} \cdot d \vec{r} \) along the line segment from \( (2,4) \) to \( (-3,7) \). (Either method is fine, directly from the definition or by using \( (a) \) and the fundamental theorem...)