but...hmmm If I think what you are saying is what you are really saying then the answer is no...you cant just throw out an aspect in lieu of an easier integral
if the integrand (The thing you are taking the integral of) has a discontinuity that is an element of [a,b] where a and be are the limits of integration then the integral is improper
if the integrand (The thing you are taking the integral of) has a discontinuity that is an element of [a,b] where a and be are the limits of integration then the integral is improper
No. Consider $\displaystyle f(x) = \left\{ \begin{array}{c}-1 \mbox{ for }-1\leq x\leq 0 \\ 1\mbox{ for }0<x\leq 1 \end{array}\right. $ then $\displaystyle \int_{-1}^1 f(x) dx$ is not an improper integral.
if the integrand (The thing you are taking the integral of) has a discontinuity that is an element of [a,b] where a and be are the limits of integration then the integral is improper
What TPH is true. Note that not all discontinuities are vertical asymptotes ......