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?
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