Evaluate $\int_{0}^{\frac{\pi}{2}} \frac{\sin ^{4} x}{\sin ^{4} x+\cos ^{4} x} d x$

Let $f(x)$ be positive for all real $x$. If $I_1 = \int_{1-h}^{h} x f(x(1-x)) dx$ and $I_2 = \int_{1-h}^{h} f(x(1-x)) dx$,where $(2h-1) > 0$,then $\frac{I_1}{I_2}$ is

The value of the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \log (\sec \theta - \tan \theta) \, d\theta$ is

Let $h(x) = \int\limits_0^x {g(t)dt}$,where $g(x)$ is a differentiable and odd function $\forall x \in R$ and $g(x)$ is periodic with period $3$.
Statement $1: h(x) + h(-x) = 0$ $\forall x \in R$
Statement $2: h(x) + h(-x) = 2 \int\limits_0^x {g(t)dt}$ $\forall x \in R$
Statement $3: h(3n) = 0$ $\forall n \in I$
Then which of the following statement$(s)$ is/are true?

Evaluate the integral: $\int_{-a}^{a} x^{2}\left(\frac{e^{x^{3}}-e^{-x^{3}}}{e^{x^{3}}+e^{-x^{3}}}\right) d x$

$\int_{-\pi}^\pi \frac{2 x(1+\sin x)}{1+\cos ^2 x} d x=$