DSE 2011 Q.24

Posted by Chinni18 on Jun 21, 2012; 11:48am
URL: http://discussion-forum.276.s1.nabble.com/DSE-2011-Q-24-tp7578446.html

If a function F(x)= Integral a to b f(t)dt is increasing on an interval, then on that interval F is
convex
concave
increasing
decreasing
 Answer key says convex
But consider the following figure, where a convex combination of points related to b and c lie outside the set.
Shouldn't the answer be increasing?
I don't understand, I might be wrong, could someone shed some light on how they did this?