  In the theory of time scales, given $\mathbb{T}$ a time scale with at least
two distinct elements, an integration theory is developed using ideas already
well known as Riemann sums. Another, more daring, approach is to treat an
integration theory on this scale from the point of view of the Lebesgue
integral, which generalizes the previous perspective. A great tool obtained
when studying the integral of a scale $\mathbb{T}$ as a Lebesgue integral is
the possibility of converting the ``$\Delta$-integral of $\mathbb{T}$'' to a
classical integral of $\mathbb{R}$. In this way, we are able to migrate from a
calculation that is sometimes not so intuitive to a more friendly calculation.
A question that arises, then, is whether the same result can be obtained just
using the ideas of integration via Riemann sums, without the need to develop
the Lebesgue integral for $\mathbb{T}$. And, in this article, we answer this
question affirmatively: In fact, for integrable functions an analogous result
is valid by converting a $\Delta$-integral over $\mathbb{T}$ to a riemannian
integral of $\mathbb{R}$.
