I am truly astonished to the amount of help I received, I'd like to thank Scott, Mr. Fantastic, Chris, and TheEmptySet for all this help you guys have given me. I now feel like I'm no longer alone...

This one is also a tuffy, perhaps someone may want to show me the light?

Question:

Let C be the closed curve C1 + C2 , where C1 is given by

r1 (t) = t

**i** + t^2

**j**, o <= t <= 1

r2 (t) = (2 - t)

**i** + (2 - t)

**j** , 1 <= t <= 2

a) Draw a sketch of the curve C, with arrows to indicate orientation

*(im not sure if it's possible to do this online, but a description will be very very much appreciated)*
b) Calculate the line integral

, where F is the vector field: F ( x, y ) = x^2

**i** + x y

**j**