How Do You Calculate Probability Using a Density Function?

[mrvirgo]

A continuous random variable X has the density function
f(x)=x for 0<x<1
2-x for 1 _<x<2
0 elsewhere.
a. Show that P(0<X<2)=1
B. Find P(X<1.2).


Please see the attached file.
Thank

 

[HallsofIvy]

1. A lot of people will not open files for fear of viruses.

2. Here, there was no point in attaching the file since it doesn't say anything you haven't written here! In particular, there is not attempt at the problem youself.
How is P(a< X< b) defined for any probability density function f(x)? Where exactly is your difficulty?