Is there a general representation of $u[n-a]-u[n-b]$ in terms of unit impulses $\delta$?

Question

Consider in the discrete-time domain, the unit-step function : $$ u[n]=\begin{cases} 1&\text{if $n\geq 0$}\\ 0&\text{if $n<0$} \end{cases} $$ We know that the first-order difference equation describes a relation between the unit-impulse function and the unit-step function as follow : $$ \delta[n]=u[n]-u[n-1] $$ I was wondering that in general, how can we express a difference equation of this kind : $$ u[n-a]-u[n-b] $$ In terms of unit impulses $\delta$? With $a,b\in\mathbb{Z}^{+}$

Answer 1

$u(x)=\int\limits\limits_{-\infty}^x\delta(x)\,dx$ where $u(x)$ is the Heaviside step function and $\delta(x)$ is the Dirac delta function.

So $u(x-a)-u(x-b)=\int\limits\limits_{-\infty}^x(\delta(x-a)-\delta(x-b))\,dx$