Can someone please help me with the following question and explain their reasoning. I' m having a little trouble. Thank you so much in advance!

If there is an average value of a Continuous function f() over the interval from x = - I to 2= 7 is ? The value of S f ( x ) de ) is what ? In relation to this, utilizing the mean value theorem for integrals since f ( x ) is continuous over Elj ], there is a real number C in the interval from x = - 1 to x = 7 such that which of the following? A ) f ( 6 ) = C B ) f ( C ) = 6 ( ) f ( c ) = 3 D ) f ( 3 ) = C E ) the area under f ( x ) equals c F ) F ( 2 ) = C G ) f ( C ) = 2 H ) f ( C ) = 12