# Invariance of action integral under point transformations

I am reading Goldstein classical mechanics chapter 2 p. 35. Here the author states that the action integral $$\int L(q,\dot q,t)dt$$ is invariant under change in generalized coordinates $$q_i=q_i(s_1,...,s_n,t)\qquad i=1,...,n.$$ I can't proceed from $$\int L(q(s,t),\dot q(s,\dot s ,t),t)dt$$ How to continue from here?

Concretely, Goldstein writes under eq. (2.2):

"the Hamilton's principle is a sufficient condition for deriving the equations of motion enable us to construct mechanics of monogenic systems from Hamilton's principle as the basic postulate rather than Newton's laws of motion. such a formulation as advantages example since the integral $$I$$ is obviously invariant to the system of generalized coordinates used to express the equations of motion must always have Lagrangian form no matter how the generalized coordinates are transformed."

The main point that Goldstein here tries to convey is that the Lagrangian $$L(q,\dot{q},t)$$ is invariant under passive change of generalized coordinates. See also this, this & this related posts.