How does one know when a vector field is conservative find

Question

Consider the vector field F(x, y, z) = 2xyi + (x² + 2yz)j+ y² k.

a. Calculate the curl of F.

b. Calculate the divergence of F.

c. How does one know when a vector field is conservative?

d. Find the scalar field f(x, y, z) such that F =∇f

e. Evaluate the integral ∫_c F · dr where C is the curve defined as r(t) = ti + tj + t²k and 0 ≤ t ≤ 1.