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\[\int\limits_{0}^{5}\left| (x^2-5x+4) \right| dx\]

Thanks! How did you get those 3 parts (this is kinda dumb, but sorry).

Isn't it 0 @ 1?

yes it is because at x=0 still abs (x^-5x+4) =(0-0+4)=4 positive .

Should the second integral be from 1 to 4 instead of 1 to 3, and the third integral be from 4 to 5?

at x=1 yes zero .

so the second integral should be from 1 to 4, and the 3rd one 4 to 5?

sorry i wrote it wrong . you are right
first from 0..1 second from 1..4 and third from 4..5