$\int_{a-6}^{b-6} f(x+6) dx$ is equal to

Let $[\cdot]$ denote the greatest integer function. Then $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left( \frac{12(3+[x])}{3+[\sin x]+[\cos x]} \right) dx$ is equal to:

$\int_0^\pi x f(\sin x) dx = $

If $I = \int_{0}^{1} \frac{dx}{1+x^{\pi / 2}}$, then

The value of $\int_{-2}^{2} (ax^3 + bx + c) dx$ depends on

$\int_0^{\pi / 2} \frac{1}{1+\tan ^{2020}(x)} d x=$