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.