(iv) If and are integrable, thenare integrable and
                  

(v) If and are integrable and for all , then
                  

(vi) If is integrable on , then is integrable over every interval and
                  

      This is called the additive property of the integral.
      (we define for every ).

(vii)If and are integrable, then is also integrable.

Theorem (Mean Value Property for Definite Integrals):

If is continuous, then there is at least one point such that
                   

Average Value of a function: