Regular expression for the language accepting the strings containing at most one pair of $1$'s over $\{0,1\}$ Design a regular expression for the language accepting the strings containing at most one pair of $1$'s over $\{0,1\}$

So basically we have the language $L=\{11,011,110,0011,1100\ldots\}$.
I find the expression to be $R=(0+1)^*11(0+1)^*$.
But I found here the answer to be $R=(0 + 10)^*(11 + \epsilon)(0 + 10)^*$.
I cannot differentiate these two answers and the logic behind the later answer.
EDIT: In my answer, the first $(0+1)^*$ may provide $11$, so after this another $11$ is not permissible since at most one pair of $11$ is required. But what's the logic behind $(11+\epsilon)$?
The logic behind $(11+\epsilon)$ is to either allow a $11$, or allow no such pairs. The question states &quot;[...] containing at most one pair [...]&quot;, and therefore we need to allow either one or zero pairs, and this is achieved by $(11+\epsilon)$.