Abstract: Using the schemic Grothendieck rings introduced in my earlier talks, I will describe a new variant of motivic integration on a scheme of finite type over an algebraically closed field via the notion of arc formula(ry). In certain cases (linear singularities), this will lead to a new, characteristic-free proof of the motivic rationality of the geometric Igusa zeta series of a hypersurface, by means of a simple algorithm.