1. Integration to find cdf

For a cdf where 0<x<4 & 4<x<8 have different functions, what limits would i use?

Would it be 0-t and t-8 or 0-t and 4-t? Thanks

2. Am I missing something? Why wouldn't you use $(0,4)$ and $(4,8)?$

3. I have to integrate to find the cdf, normally when the probabilities occur between 0 and 8 you integrate between 0 and t (dummy variable) but here I dont know whether to integrate between 0 and t and then 4 and t or not?

4. The cdf defined as

$\int _{- \infty} ^ t f(t) \ dt$

In this case, you are integrating a piecewise function, which hopefully you know how to do - presumably your cdf will also be piecewise. Incidentally, you should note that your pdf is always going to be defined over the entire real line, so this integral always makes sense; if it seems like it isn't defined on a particular subset of the real numbers, it is taken to be identically 0 there.