Maximally extend integer intervals
Haskell, 145 bytes

import Data.List
x=maximum.map length.filter(nub&gt;&gt;=(==)).map concat.sequence.map(\[a,b]-&gt;[[2*a-b-1..b],[a..b],[a..2*b-a+1]]).read.('[':).(++"]")


Sample runs:

λ: x ""
0

λ: x "[5,6]"
4

λ: x "[-3,0],[1,2],[4,9]"
22