Suppose $F\left(x\right)$ is an antiderivative of $f\left(x\right)$. Which of the following statements about the indefinite integral $\int f\left(x\right) dx$ is true?

For the following function $f\left(x\right)$, find the antiderivative $F\left(x\right)$ that satisfies the given condition.

$f\left(x\right)=5x^4$; $F\left(0\right)=1$

For the following function $f\left(x\right)$, find the antiderivative $F\left(x\right)$ that satisfies the given condition.

$f\left(x\right)=100x^{99}$; $F\left(1\right)=101$

Find all functions whose derivative is f'(x) = x + 1.

Suppose the graph of a function $f$ is shown below. Which of the following graphs could represent an antiderivative $F$ of $f$?

If $F\left(x\right)$ and $G\left(x\right)$ are both antiderivatives of $f\left(x\right)$, what must be true about $F\left(x\right)$ and $G\left(x\right)$?

Which of the following is an antiderivative of $2x$?

Which of the following is an antiderivative of $f\left(x\right)=tan(e^x+2)$ on $0\le x\le ln\left(2\right)$?

Which of the following is an antiderivative of $f\left(x\right)=\cos (x^2-5)$?