$\int_{-3}^{3} \frac{x^2 \sin x}{1 + x^6} \, dx = $

Value of the definite integral $\int_{-3}^{1} (2(t+1)^5 - 5(t+1)^3 + t + 3) dt$ is equal to

Evaluate the definite integral: $\int_0^\pi \frac{x \cos^2 x}{1+\sin x} dx$

For $n > 0,$ $\int_0^{2\pi } {\frac{{x{{\sin }^{2n}}x}}{{{{\sin }^{2n}}x + {{\cos }^{2n}}x}}\,dx = } $

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?

$\int_{-1}^1 \frac{\sqrt{1+x+x^2}-\sqrt{1-x+x^2}}{\sqrt{1+x+x^2}+\sqrt{1-x+x^2}} dx$ is equal to