How do I integrate this equation?

[vorcil]

http://img717.imageshack.us/img717/4568/integral3.jpg

I can see how to get to

http://img179.imageshack.us/img179/3193/integral1.jpg

but I'm not sure how the integral works

I can integrate normal linear equations, trigonometric equations ect..

someone please show me qualitatively

 

[ystael]

$$F_x(x, 0)$$ means the $$x$$-component of $$\mathbf{F}$$ at the point $$(x, 0)$$. Since $$\mathbf{F}(x, y) = (y, 2x)$$, you compute $$\mathbf{F}(x, 0) = (0, 2x)$$, therefore $$F_x(x, 0) = 0$$. The computation of $$F_y(1, y)$$ is similar.