Why do you need integration? It's a triangle with Height = 1 and Base = 2. You can set up the integration if you like.
Notice also how it is nice and symmetrical about the line x = 1. This puts 50% of the probability on each side, making Pr(x < 1.2) = ½ + Pr(1 < x < 1.2). For the last piece, you can:
1) Set up the integration of 2-x on [1,1.2]
2) Remember the area of a trapezoid on [1,1.2]
3) Spot the triangle on [1.2,2] and compute its area, making the desired probabiltiy ½ - (Area of Triangle)
This kind of thing always makes me nervous. Maybe you are thinking about it, but it feels like you just want to memorize the procedure rather than understand what you are doing. There is no substitute for understanding. Please review what I said above and see that it is encouragement for you to think about the ideas, not just the processes.want the solution with step by step method. Please mention every step