1.
F=<x,y^2>
Drawn vector field extends out from origin
To right of origin, vectors slowly increase
in magnitude as distance from origin increase, while the direction
depends on if they were to the right of the origin or left. 
The further north from origin vector field travels, the greater 
the vectors increase in magnitude. South of the origin, the vectors 
are much larger and face towards the origin; they slowly begin 
to face away from origin as one moves left or right of the origin. 

2.
F=<ycos(xy),xcos(xy)>
= cos(yx)-yxsin(xy)
= cos(xy)-xysin(xy)
cos(xy)-xysin(xy)+C=f(x,y)