As I said I think the integration is not quite correct. at 2.70 there are 2 hydrogens attached.
The lines tell you how many hydrogen atoms are on the adjacent carbon atom, formula n+1, where n is the number of hydrogens. The intensity of the lines follows Pascal's triangle, 1, 1,1 1, 2, 1, 1,3,3,1 and so on. So for example if you saw 4 lines with intensities of 1,3,3,1 (a quartet) it's neighbouring C atom has 3 hydrogens attached to it. That is n+1 where n is the number of neighbouring hydrogens.