Calculus - Definite Integrals

Let $f(x)$ be a continuous function defined in $[0,2] \rightarrow \mathbb{R}$ and satisfying the equation $\int_{0}^{2} f(x)[x - f(x)]dx = \frac{2}{3}$. The value of $f(1)$ is

The value (round off to one decimal place) of $\int_{-1}^{1} x e^{|x|} dx$ is

Consider the following definite integral: $I = \int_0^1 \frac{(\sin^{-1} x)^2}{\sqrt{1-x^2}} dx$ The value of the integral is