Line integrals of vector fields

Question

Assignment:

Let γ be given on 0 ≤ u ≤ 1 by (x,y)=(1-u,u) The vector field (F₁(x , y),F₂ (x , y)) is a gradient field.

Compute:

∫_γ (F₁dx+F₂dy) Where:

F₁ = xy²

F₂ = x²y

Provide complete and step by step solution for the question and show calculations and use formulas.