Proving a property of the integral If $ f $ is Riemann integrable on $[a,b]$ and if $a<c<b$, then $ f $ is Riemann integrable on $[a,c]$ and on $[c,b]$. Also, $\int^c_a f dt+\int^b_c f dt=\int^b_a f dt$. 
I can prove the first part (that $ f $ is Riemann integrable on $[a,c]$ and on $[c,b]$)  but can't come up with a way to prove the second part.

If you have any partition on $[a,b]$, you can include $c$; this just lowers the upper sum a bit and raises the lower one a bit.  See if you can use this to argue your conclusion.
