I'll do it in ID then, how would I do this?
From memory, if you highlight the text with the text selection tool in ID, then the fill colour will apply to the text. If you select the text box with the object selection tool (black arrow) and pick a fill colour, it will apply to the box itself.
Also: the colour palette will show a 'T' if you're dealing with text colours, rather than box colours.
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Edit to add:
However, the above will fill the whole text box, rather than apply a background to the text itself, dependent upon the line-length. So, you would need to create a separate text box for each line to achieve the effect in the original post.
Personally, I was always taught to put a separate box behind the text rather than fill the text box itself and -- although that advice came to me working with Quark 3.31 -- it still works for me ...
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Cheers
Jim