I wish to create a Mathematica module that would take as input a Mathematica-defined probability distribution D and will perform an integration over the support of its density f, $supp(f)$ (where $f:Xsubseteqmathbb{R}rightarrowleft(0,1right)$). How to find the lower and upper bounds $s_1, s_2$ of the set:

$suppf=left{ xin X:,fleft(xright)>0right} =left(s_{1},s_{2}right)$

For example, I am looking for a (perhaps already defined) Mathematica function such that if supplemented with UniformDistribution({1, 2}) to return s1=1 and s2=2. Thank you for any inputs!