maths urgent

[gauri]

let f be a real valued differentable function defined for all x>=a.
consider F defined by F(x)= integration f(t) dt from a to x.
if f is increasing on any interval,then on that interval F is:

convex
concave
increasing
decreasing.

the answer is convex but someone please explain how and why?

[AYAN]

Since f(t) is the slope of F and it is increasing hence F will be convex
though it may be increasing or decreasing......