Behavior of Accumulation Functions Involving Area Practice Test

Define $F(x)=\int_{0}^{x} f(t),dt$. If $f(x)>0$ for $0<x<2$ and $f(2)=0$ with no sign change, what is true about $F$ at $x=2$?

Define $G(x)=\int_{1}^{x} g(t),dt$. If $g(x)>0$ for all $x$ and $g(3)=g(5)$, what must be true about $G$ on $(1,6)$?