Question related to Integration and Probability Density Functions My question is regarding integration questions related to the probabilities of continuous random variables.
If X = 0  to 5 is represented by f1(x) and X=5 to 10 is represented by f2(x) and we want P(0<=X<=10). Would the answer be integral over 0 to 5 for f1(x)  + integral of 5 to 10 for f2(x)? That is I am confused when we are to calculate probabilities that are represented by 2 sets of functions. Also are the endpoints exclusive or inclusive to probability calculations? If I calculate the integral of 0-10 will 0 and 10 be included as probabilities? I am guessing though that for continuous RV's P(0<=X<=10) is the same as any combination of <=,>=,<,> as after all they cannot take discrete values.
Any help would be appreciated.

Yes to your first question:  You have it right about integrating each function in the range in which it applies.  For example:
$$
f(x) =\left\{ \begin{array}{cc} \frac{x^2}{144} & 0\leq x<6 \\
\frac{x}{64} & 6 \leq x \leq 10 \end{array} \right. 
$$
Then 
$$P(2<x<7) = \int_2^6  \frac{x^2}{144} dx + \int_6^7 \frac{x}{64} dx
$$
For the question about discrete values:  If the functions $f(x)$ involve no $\delta$-functions, that is, if the distribution has no discrete properties, then inclusion or exclusion of the endpoints does not matter.
