$\int_{0}^{\pi} \frac{\cos ^{4} x}{\cos ^{4} x+\sin ^{4} x} d x$ is equal to

If $m, l, r, s, n$ are integers such that $9 > m > l > s > n > r > 2$ and $\int_{-2 \pi}^{2 \pi} \sin ^m x \cos ^n x \, dx = 4 \int_0^\pi \sin ^m x \cos ^n x \, dx$,$\int_{-\pi}^\pi \sin ^r x \cos ^s x \, dx = 4 \int_0^{\pi / 2} \sin ^r x \cos ^s x \, dx$ and $\int_{-\pi / 2}^{\pi / 2} \sin ^l x \cos ^m x \, dx = 0$,then which of the following is true?

Let $J = \int_0^1 \frac{x}{1+x^8} dx$. Consider the following assertions:
$I$. $J > \frac{1}{4}$
$II$. $J < \frac{\pi}{8}$
Then,

If $f(x) = \int_1^x \frac{1}{2+t^4} dt$,then

Let the domain of the function $f(x) = \log_{4}(\log_{5}(\log_{3}(18x - x^{2} - 77)))$ be $(a, b)$. Then the value of the integral $\int_{a}^{b} \frac{\sin^{3} x}{\sin^{3} x + \sin^{3}(a + b - x)} dx$ is equal to $.....$

By using the properties of definite integrals,evaluate the integral $\int_{0}^{1} x(1-x)^{n} d x$.