Let $f(x)=|x-1|, g(x)=[x]$ and $h(x)=f(x) g(x)$ where [.] is greatest integer function.

What is $\int_{0}^{2} h(x) dx$ equal to?

Consider the following for the next two (02) items that follow:

Let $3f(x) + f\left(\frac{1}{x}\right) = \frac{1}{x} + 1$

What is $8\int_1^2 f(x)dx$ equal to?

Consider the following for the next items that follow:

Let $\displaystyle I=\int_{-2 \pi}^{2 \pi} \frac{\sin ^4 x+\cos ^4 x}{1+3^x} d x$

Consider the following for the next items that follow:

Let $\displaystyle I=\int_{-2 \pi}^{2 \pi} \frac{\sin ^4 x+\cos ^4 x}{1+3^x} d x$