Chapter 7.8, Problem 1QCE

In each part, determine whether the integral is improper, and so if so, explain why. Do not evaluate the integrals.

$\begin{array}{l}\left(\text{a}\right){\displaystyle {\int }_{\pi /4}^{3\pi /4}\cot xdx}\\ \left(\text{b}\right){\displaystyle {\int }_{\pi /4}^{\pi }\cot xdx}\\ \left(\text{c}\right){\displaystyle {\int }_0^{+\infty }\frac{1}{x^2-1}}dx\\ \left(\text{d}\right){\displaystyle {\int }_1^{+\infty }\frac{1}{x^2-1}dx}\end{array}$