Definite Integration

What is $\int_2^8|x-5| d x$ equal to?

What is $\int_0^{8 \pi}|\sin x| d x$ equal to?

Let $f(x)=|x-1|, g(x)=[x]$ and $h(x)=f(x) g(x)$ where [.] is greatest integer function. What is $\int_{-1}^0 h(x) d x$ equal to?

Paragraph: Let $l=\int_a^b \frac{|x|}{x} d x, \quad a \lt b$ Question: What is $l$ equal to when $a \lt 0 \lt b$ ?

What is $\int_0^{\frac{\pi}{2}} e^{\ln (\cos x)} d x$ equal to?

Paragraph: Consider the integrals $\mathrm{I}_1=\int_0^x \frac{x d x}{1+\sin x} \text { and } \mathrm{I}_2=\int_0^\pi \frac{(\pi-x) d x}{1-\sin (\pi+x)}$ Question: What is the value of $\mathrm{I}_1+\mathrm{I}_2$ ?

Paragraph: Let $f(t)=\ln \left(t+\sqrt{1+t^2}\right)$ and $g(t)= \tan (f(t))$. Question: What is $\int_{-\pi}^\pi g(t) d t$ equal to?

What is $\int_{-2}^{-1} \frac{x}{|x|} d x$ equal to?

If $f(x)$ satisfies $f(\mathrm{l})=f(4)$, then what is $\int_1^4 f^{\prime}(x) d x$ equal to?

If $f(x)=2^x$, then what is $\int_2^{10} \frac{f^{\prime}(x)}{f(x)} d x$ equal to?

What is $\int_0^1 \ln \left(\frac{1}{x}-1\right) d x$ equal to?

What is $\int_0^{\frac{\pi}{4}} \frac{d x}{(\sin x+\cos x)^2}$ equal to?