If f has a discontinuity at c, where a<c<b, and both `int_a^c f(x)dx` and `int_c^bf(x)dx` are convergent, then `int_a^b f(x)dx=int_a^c f(x)dx+int_c^b f(x)dx`. Only when BOTH integrals are convergent, convergent is `int_a^b f(x)dx`. Otherwise it is divergent.