The value of  ∫−13 {|x−2|+[x]}dx, where x denotes the greatest integer less than or equal to x is

∫−13 {|x−2|+[x]}dx=∫−10 {|x−2|+[x]}dx+ ∫01 {|x−2|+[x]}dx+∫12 {∣x−2∣+[x]}dx+∫23 {|x−2|+[x]}dx=∫−10 (2−x−1)dx+∫01 (2−x+0)dx+∫12 (2−x+1)dx+∫23 (x−2+2)dx=x−x22−10+2x−x2201+3x−x2212+x2223=−−1−12+2−12+(6−2)−3−12+92−2=7