Functions without Antiderivatives as Known Combination of Basic Functions

Q. If $f\left(x\right)$ and $g\left(x\right)$ are inverse function of each other such that $f\left(1\right)=3$ & $f\left(3\right)=1$, then ${\int }_1^3(g\left(x\right)+\frac{x}{f^{\prime }\left(g\right(x\left)\right)})dx$ is equal to

Q. Antiderivative of all the continuous functions can be written in terms of elementary functions

1. False
2. True

Q. Let $g\left(x\right)=\underset{0}{\overset{x}{\int }}f\left(t\right)dt$, where $f$ is such that $\frac{1}{2}\le f\left(x\right)\le 1$ for $t\in [0,1]$ and $0\le f\left(t\right)\le \frac{1}{2}$ for $t\in [1,2]$ Then, $g\left(2\right)$ satisfies the inequality

1. $-\frac{3}{2}\le g\left(2\right)<\frac{1}{2}$
2. $0\le g\left(2\right)<2$
3. $\frac{1}{2}\le g\left(2\right)\le \frac{3}{2}$
4. $2<g\left(2\right)<4$