∫[1→5] (|2-x|+|sinx|) dx
=∫[1→5] |2-x| dx+∫[1→5] |sinx| dx
=∫[1→2] (2-x) dx+∫[2→5] (x-2) dx+∫[1→π] sinx dx-∫[π→5] sinx dx
=(2x-(1/2)x²) |[1→2] + ((1/2)x²-2x) |[2→5] -cosx |[1→π] + cosx |[π→5]
=4-2-2+1/2+25/2-10-2+4-(-1-cos1)+cos5-(-1)
=7+cos1+cos5
∫[1→5] (|2-x|+|sinx|) dx
=∫[1→5] |2-x| dx+∫[1→5] |sinx| dx
=∫[1→2] (2-x) dx+∫[2→5] (x-2) dx+∫[1→π] sinx dx-∫[π→5] sinx dx
=(2x-(1/2)x²) |[1→2] + ((1/2)x²-2x) |[2→5] -cosx |[1→π] + cosx |[π→5]
=4-2-2+1/2+25/2-10-2+4-(-1-cos1)+cos5-(-1)
=7+cos1+cos5