Which of the following definite integrals are equal to $0$?

Write the two definite integrals subtracted below as a single integral.

${\int }_1^6\sqrt{x^2-5x}dx-{\int }_{10}^6\sqrt{x^2-5x}dx$

Evaluate the following definite integral.

${\int }_{100}^{100}\frac{\sin \left(2x\right)-100x^2}{\sqrt{x^5+\tan (3x-6)}}dx$

Which of the following integrals represents the area of the region bounded by the curves $y=x^2$ and $y=4$ between $x=0$ and $x=2$?

Which of the following limits is equal to the definite integral from $2$ to $5$ of $1+x^4$ $dx$?

Which of the following definite integrals is equal to the area under the curve $y=x^2$ from $x=0$ to $x=2$?

What is the average (mean) value of the function $3t^3-t^2$ over the interval $1\le t\le 2$?

For the function shown below, the definite integral from $1$ to $0$ of $f\left(x\right)$ $dx$, that is, ${\int }_0^{1}f\left(x\right)dx$, is closest to which of the following values?

Let $g\left(x\right)={\int }_0^{x}f\left(t\right)dt$, where $f$ is the function whose graph is shown. Which of the following statements is true about $g\left(x\right)$?