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.

If $X$ admits a density $f$ which a piecewise continuous function over $[0,10]$ such that 
$$
f(x) =
\begin{cases}
f_1(x),  & \text{if $0\leq x \leq 5$,} \\[2ex]
f_2(x), & \text{if $5\leq x \leq 10,$}
\end{cases}
$$ then
$$
P(0\leq X\leq10)=\int_0^5f_1(x) \:dx+\int_5^{10}f_2(x) \:dx.
$$ Since $f_1$ and $f_2$ are continuous, you get 
$$
P(0< X\leq10)=P(0< X<10)=P(0\leq X\leq10)=\cdots,
$$ resulting from
$$
\int_a^af_1(x) \:dx=0=\int_b^bf_2(x) \:dx, \quad a,b \in [0,10].
$$
