Let $X = { x_1, x_2, dots, x_n }$ be the (multi-)set of elements in your subset-sum instance and let $t$ be the target value.

Create the undirected graph $G=(V,E)$ where $V={a,b} cup X$ and $E = ( {a,b} times X) cup {(a,b)}$.

The weight of edge $(a, x_i)$, for $x_i in X$, is $x_i$. The weight of edge $(b, z)$ for $z in {a} cup X$ is $0$. Finally, pick $l=u=t$.

There is some $Y subset X$ such that $sum_{x_i in Y} x_i = t$ if and only if there is a spanning tree $T$ of $G$ of total weight between $l$ and $u$.

Indeed, given $Y$, you can select $T$ as the tree induced by the edges in ${(a,x_i) mid x_i in Y} cup {(b,z) mid z in V setminus Y}$.

Moreover, given a tree $T=(V,F)$ of total weight between $l$ and $u$, you can select $Y = { x_i mid (a,x_i) in F }$.