Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2014 / Paper 2 / 9

Only the $x$ component of the vector field is nonzero, so $\mathbf{F}\cdot d\mathbf{r}=(x^2+y^2)dx$. On the vertical segment, $dx=0$ throughout. Hence

On the horizontal segment $y=0$, while $x$ decreases from $1$ to $-1$. Keeping this orientation givesThe minus sign follows from traversing opposite to the positive $x$ direction.