Use this result to find the work done if this force field moves an object from the point (-2,3) along the piecewise linear path to (1,3), and from there to (2,4).

Work is the product of force and the distance to which the force acts along. 

W = Fd

We can find the distance, but we can't find W if we don't know F. Since it is not mentioned in the problem, we really can't solve this. But as an example, we can assume F to be 1 N. Now, the formula for distance is:

d = √(x₂ - x₁)² + (y₂ - y₁)²
d₁ = √(1 - -2)² + (3 - 3)² = 3 
d₂ = √(2 - 1)² + (4 - 3)² = √2

Hence,
W = (1 N)(3 + √2) = 4.41 J