$($a$)$ Assume f$($x$)$ is continous on a $<=$ x $<=$ b$,$ and consider the average S with all points x$\_$j in the interval $[$a$,$b$].$ Show that S$=$f$($l$)$ for some l in $[$a$,$b$]$

$($b$)$ Generalize part $($a$)$ to the sum S with all x$\_$j in $[$a$,$b$]$ and all w$\_$j $>=0$

I did part $($a$)$ using intermediate value theorem, but not sure if my answer is correct. Can't figure out how to do part $($b$).$