I hope that by "Fd" you mean the integral of the dot product of the vector force, F, and vector, d, from (0, 1, 0) to (1, 0, 3).
As for the "other method", Is it possible that this vector field is "conservative"? That is, that there exist some function, such that ? If that is true then the is the "potential function" and the work done is . How can you check that? How can you find from F?