Show that a function is increasing at a given interval

Question

enter image description hereSo i have this function (integral) of F(x)=integral tending from x(on top) to 0(on bottom) et² dt.

The question asks to show that the function is convex upward in [0, +∞).

How do i do that ? I was thinking of computing the integral with the boundaries. Then compute the derivative? I am not sure how to proceed.

Can somebody help ?

Answer 1

$$F''(x)=(e^{x^2})'=2xe^{x^2}\geq0.$$