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.

We have $p \{x\} = \int_{\{x\}} f(t) dt = 0$, so you have
$p [a,b] = p[a,b) = \dots$, that is, the addition of removal of single (in fact countable, if you want) point 
will not change the value of the probability.
In your case, you can define $f(x) = \begin{cases} f_1(x), & x \in [0,5) \\
f_2(x), & x \in [5,10] \end{cases}$ and so the probability will be
$p [0,10] = \int_{[0,10]} f(t) dt$.
