Calculate a CDF given two PDFs. I have two PDF's, $f_1(x)$ and $f_2(x)$ and I need to find the CDF (not PDF) of $f_3(x)$ where    
$f_3(x) = \frac{1}{2} (f_1(x) + f_2(x))$  
I have already calculated $F_1$ and $ F_2$, the CDF's of $f_1$ and $f_2$ respectively. 
Can I simply take half the sum of the two CDF's as follows
$F_3(x) = \frac{1}{2}( F_1(x) + F_2(x))$   
or do I instead need to compute $f_3$ and then calculate $F_3$ from there? 

The pdf and cdf are  related by $F(x) = \int_{-\infty}^x f(t) dt$.
In your case
\begin{eqnarray}
F_3(x) &=& \int_{-\infty}^x f_3(t) dt  \\
&=& \int_{-\infty}^x \frac{1}{2}(f_1(t)+f_2(t)) dt \\
&=& \frac{1}{2} \left(\int_{-\infty}^x f_1(t) dt + \int_{-\infty}^x f_2(t) dt \right) \\
&=& \frac{1}{2} (F_1(x) + F_2(x))
\end{eqnarray}
