I am trying to prove that if $\displaystyle a<c<b$, then $\displaystyle \int _{a}^{b}f=\int _{a}^{c}f+\int _{c}^{b}f$. This fact is very easy for me to visualize but I'm not sure how to get started.

My professor talked about restricting the function and only evaluating the integral on a smaller interval. I feel like this might be key to proving it but I'm not sure how to tie it together. Any help would be appreciated.