Consider a force $$\vec{F} = -x\hat{i} + y\hat{j}$$. The work done by this force in moving a particle from point $$A(1,0)$$ to $$B(0,1)$$ along the line segment is: (all quantities are in SI units)

$$W = \int \vec{F} \cdot d\vec{r} = \int (-x\,dx + y\,dy)$$

Equation of the line segment from $$A(1,0)$$ to $$B(0,1)$$:

$$y - 0 = \frac{1 - 0}{0 - 1}(x - 1) \implies y = -x + 1 \implies x + y = 1$$

$$dx + dy = 0 \implies dx = -dy$$

$$W = \int_{1}^{0} -x\,dx + \int_{0}^{1} y\,dy$$

$$W = \left[ -\frac{x^2}{2} \right]_1^0 + \left[ \frac{y^2}{2} \right]_0^1 = \left(0 - \left(-\frac{1}{2}\right)\right) + \left(\frac{1}{2} - 0\right) = \frac{1}{2} + \frac{1}{2} = 1$$