Suppose $f$ is such that $f(-x) = -f(x)$ for every real $x$ and $\int_{0}^{1} f(x) dx = 5$,then $\int_{-1}^{0} f(t) dt = $

Assertion $(A)$: $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{(\sin x)^{\sqrt{2}} dx}{(\sin x)^{\sqrt{2}}+(\cos x)^{\sqrt{2}}} = \frac{\pi}{12}$
Reason $(R)$: $\int_{a}^{b} \frac{f(x) dx}{f(x)+f(a+b-x)} = \frac{b-a}{2}$

The value of the integration $\int_{-\pi / 4}^{\pi / 4} (\lambda|\sin x| + \frac{\mu \sin x}{1+\cos x} + \gamma) \, dx$

If $I_n = \int_{-\pi}^{\pi} \frac{\sin(nx)}{(1+\pi^x) \sin x} dx$,$n=0, 1, 2, \ldots$,then
$(A)$ $I_n = I_{n+2}$
$(B)$ $\sum_{m=1}^{10} I_{2m+1} = 10\pi$
$(C)$ $\sum_{m=1}^{10} I_{2m} = 0$
$(D)$ $I_n = I_{n+1}$

Let $f(x) = \frac{\sin x}{x}$,then $\int_{0}^{\frac{\pi}{2}} f(x) f\left(\frac{\pi}{2} - x\right) dx =$

The value of $\int_{-1}^{1} x^{2} e^{[x^{3}]} dx$,where $[t]$ denotes the greatest integer $\leq t$,is