A <uniform distribution> has constant <probability density> on its interval, and the integral of that density must be one. The interval has length one, so
$$
\boxed{g(y)=\begin{cases}1,&-1/2\leq y\leq1/2,\\0,&\text{otherwise}.\end{cases}}
$$
Changing either endpoint value has no effect on the <probability distribution>.

Solution

Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2019 / Paper 2 / 14 / d / i / Solution

 Solution (source code)