Answer
The applied force does -209 J of work during the cow's displacement.
Work Step by Step
$W = \int_{0}^{6.9~m}F_x~dx$
$W = \int_{0}^{6.9~m}-((20.0~N)+(3.0~N/m)~x)~dx$
$W = -(20.0~N)~x -(1.5~N/m)~x^2\vert_{0}^{6.9~m}$
$W = -(20.0~N)(6.9~m) -(1.5~N/m)(6.9~m)^2$
$W = -209~J$
The applied force does -209 J of work during the cow's displacement.