The problem you provided asks to determine the maximum and minimum values of the function:

$f(x, y) = x^2y + xy^2 + x^3 - x$

subject to the domain $D$ where:

$D = \{(x, y) : x \geq 0, y \geq 0, x + y \leq 4\}$

This is a constrained optimization problem, and the method of substitution is likely referring to handling the constraints via substitution or Lagrange multipliers. To solve it, we will need to:

1. Examine the critical points within the domain.
2. Evaluate the boundary points defined by $x + y = 4$.
3. Use appropriate methods such as Lagrange multipliers or substitution for the constraint.

Would you like me to go step-by-step through this solution process?