$(10$ points$)$ Mike was asked to evaluate the integral $I={\displaystyle \underset{0}{\overset{10}{}}}\frac{a+1}{x^2-(a-1)x-a}dx$ Below is his solution:

$\frac{a+1}{x^2-(a-1)x-a}=\frac{a+1}{(x-a)(x+1)}=\frac{1}{x-a}-\frac{1}{x+1}$

$I={\displaystyle \underset{0}{\overset{10}{}}}\frac{1}{x-a}dx-{\displaystyle \underset{0}{\overset{10}{}}}\frac{1}{x+1}dx=ln|x-a|{|}_0^{10}-ln|x+1|{|}_0^{10}$

$I=ln|10-a|-ln|a|-ln11+ln1=ln(\frac{|10-a|}{11|a|})$

Explain why Mike's solution cannot be considered as a right one. Correct his answer. Do not integrate!