F2 is continuous everywhere so it cannot mask f1 s jump at x equals 1 only right continuity survives

Consider the following real-valued functions $F_{1}$ and $F_{2}$ defined on $\mathbb{R}$, given by $F_{1}(x)=1$ if x≥1, 0 otherwise, and $F_{2}(x)=\int_{0}$ˣexp(−t)dt if x≥0, 0 otherwise. Define another function $F:\mathbb{R}\to[0,1]$ by $F(x)=(2/3)F_{1}(x)+(1/3)F_{2}(x)$ for all $x\in\mathbb{R}$. Which of the following statements are true?