Given the vector field vec$(F)(x,y)=(4y-7x^2)vec()+(4x+5y)vec()$

$(a)$ Show that vec$(F)(x,y)is$ conservative. $(5$ points$)$

$(b)$ Find its potential function, pointsC $is$ a smooth curve

from $(-1,3)to(2,-5).(7\mathrm{.}5$ points$)$

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}(4y-7x^2)dx+(4x+5y)dy$