The values of $b$ and $c$ for which the identity $\mathrm{f}(x+1)-\mathrm{f}(x)=8 x+3$ is satisfied, where $\mathrm{f}(x)=\mathrm{b} x^2+\mathrm{c} x+\mathrm{d}$, are

For a real number $x,[x]$ denotes the greatest integer less than or equal to $x$. Then the value of

$$ \begin{array}{r} {\left[\frac{1}{2}\right]+\left[\frac{1}{2}+\frac{1}{100}\right]+\left[\frac{1}{2}+\frac{2}{100}\right]+\left[\frac{1}{2}+\frac{3}{100}\right]+} \left[\frac{1}{2}+\frac{99}{100}\right]= \end{array} $$

The function defined by $\mathrm{f}(x)=\frac{2 x+3}{3 x+4}, x \neq-\frac{4}{3}$ is

Range of the function $\mathrm{f}(x)=\frac{x^2+x+2}{x^2+x+1}, x \in \mathbb{R}$ is