List - $I$ P. $\,\,\,\,$ The number of polynomials $f(x)$ with non-negative integer coefficients of degree $\le 2$, satisfying $f(0)=0$ and $$\int_0^1 {f\left( x \right)dx = 1,}$$ is Q. $\,\,\,\,$ The number of points in the interval $$\left[ { - \sqrt {13} ,\sqrt {13} } \right]$$ at which $$f\left( x \right) = \sin \left( {{x^2}} \right) + \cos \left( {{x^2}} \right)$$ attains its maximum value, is R. $\,\,\,\,$$$\int\limits_{ - 2}^2 {{{3{x^2}} \over {\left( {1 + {e^x}} \right)}}dx}$$ equals S. $\,\,\,\,$$${{\left( {\int\limits_{ - {1 \over 2}}^{{1 \over 2}} {\cos 2x\log \left( {{{1 + x} \over {1 - x}}} \right)dx} } \right)} \over {\left( {\int\limits_0^{{1 \over 2}} {\cos 2x\log \left( {{{1 + x} \over {1 - x}}} \right)dx} } \right)}}$$ List $II$ 1. $\,\,\,\,8$ 2. $\,\,\,\,2$ 3. $\,\,\,\,4$ 4. $\,\,\,\,0$