Since IntegerDigits has attribute Listable, there's no need to Map IntegerDigits onto Range[100]^2. Thus simply;

 ListLinePlot[First /@ IntegerDigits[Range[100]^2]]

Hello Peter, the ;; is a short form for "All" but is a very simple way to manipulate array without explicit index. have a look at the Mathematica help about Span it is very clearly explained. BTW in that particular case, Paul's proposal is even cleaner because there are no reference to table indexes at all.( /@ being the prefix form for "Map"..see also Map help)

Thank-you Christian. Definitely better. Or at least it will be if I can figure out what the [[;; , -1]] is all about.