Don't remember how work works.

This was on a GRE practice test:

Let F be a constant unit force that is parallel to the vector (-1,0,1) in xyz-space.  What is the work done by F on a particle that moves along the path given by (t,t^2,t^3) between time t=0 and time t=1?

What I want to say is (integrals are from 0 to 1) :

W = ʃF ds
= ʃ(-1/√2,0,1/√2)•(1,2t,3t^2)dt
= ʃ(-t/√2+3t^2/√2)dt
= 0

That's the right number, but is that the way to do it?

That looks right, except that
-1/√2•1 =/= -t/√2