Definite integral

Which of the positive values of a real number $a$ makes the equality $\underset{a}{\overset{7}{\int }}\frac{6x-5}{3x^2-5x}\mathrm{d}x=\ln 56$ true?

The picture shows graphs of two quadratic functions $f_1(x)$ and $f_2(x)$. Find the unknown real positive constant $a$ (as shown in the picture) such that the value of the definite integral $\underset{-1}{\overset{1}{\int }}{f}_1(x)\mathrm{d}x$ is greater by $8$ than the value of the definite integral $\underset{-1}{\overset{1}{\int }}{f}_2(x)\mathrm{d}x$.

Evaluate the following definite integral. $$\underset{-2}{\overset{0}{\int }}(1-|x+1|)\mathrm{d}x$$

Any positive real number $x$ can be written as $x=c+d$, where $c$ is an integer and $d\in [0,1)$. Then $c$ is called the integer part of $x$ and is denoted by $\left[x\right]$. Evaluate the following definite integral. $$\underset{3.1}{\overset{\frac{7}{2}}{\int }}\left[x\right]\mathrm{d}x$$