Finding C_2 for Curve F in Triangle C

[stratusfactio]

Homework Statement

F=<xy, x-y> and C is the triangle joining (1,0), (0,1) and (-1,0) in the clockwise direction.

Homework Equations

How do I have the second part of this curve?

The Attempt at a Solution

Apparently, there should only be a sum of two integrals. So I got that curve one could be
$$C_1: x=t, y=0, -1≤ t ≤ 1$$

But I have no idea how to find $$C_2$$. There's no other way, that I see, that you can take such that you keep x constant and let y vary.

 

[tjackson3]

The reason it should only be a sum of two integrals is because the line integral is just zero on the curve you have. You're only interested in the sum of the integral over $C_2$ and $C_3$. How might you parametrize those? For example, if you wanted to find a line in x-y coordinates to go from (1,0) to (0,1), you would find its slope (-1) and its y-intercept (1). The line would be y = 1-x. So if you let x = t, then what would y be and what would t vary between?