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?