Finiteness of Leaps in the sense of Hasse-Schmidt of reduced rings

We give sufficent conditions for a derivation of a $k$-algebra $A$ of finite type to be $\mathrm{\infty }$-integrable in the sense of Hasse-Schmidt, when $A$ is a complete intersection, or when $A$ is reduced and $k$ is a regular ring. As a consequence, we prove that, if in addition $A$ contains a field, then the set of leaps of $A$ is finite along the minimal primes of certain Fitting ideal of ${\mathrm{\Omega }}_{A\mathrm{/}k}$.