A continuous random variable X that can assume values between x=2 and x=4 has a density function given by
f(x)=x+1/8
Show that P (2<x<4) =1
Find P(X<3.5)
Integrate f(x) from 2 to 4 and you get an answer of 6.25, not 1. Therefore, it is not a correct pdf. However, if you meant $\displaystyle f(x)=\frac{x+1}{8}$, it does satisfy having an integral of one. To find the probability that x is less than 3.5, integrate the pdf from 2 to 3.5.