If I have a force F=4i+2xi acting on a particle going in a straight line from (0,0) to (1,1), then the work done on the particle should be the integral of 4 dx from 0 to 1  plus the integral of 2x dy from 0 to 1.  Since the particle is essentially moving along y=x, is it true that I should write 2y dy in place of 2x dy so that the work done is 4x from 0 to 1 plus y^2 from 0 to 1, or a total of 5?