Compute the superset
R + intervals, 90 87 81 bytes



function(...)t(reduce(Intervals(rbind(...),type="Z")))+c(1,-1)
library(intervals)


Try it online!

Input is a list of intervals. -Inf and Inf are R built-ins for minus/plus infinity. Output is a matrix of columns of intervals.

Not usually a fan of using non-standard libraries but this one was fun. TIO doesn't have intervals installed. You can try it on your own installation or at https://rdrr.io/snippets/ 

The intervals package supports real and integer (type = "Z") intervals and the reduce function is a built-in for what the challenge wants, but the output seems to default to open intervals, so close_intervals +c(1,-1) is needed to get the desired result.

Old version had examples in list of lists which might be convenient so I've left the link here.