An improper integral with a single infinite singularity at an endpoint \(c\), like \(\int_a^c f(x)\,dx\) or \(\int_c^b f(x)\,dx\), can be interpreted as a single limit of definite integrals, as long as the interval (namely, \([a,c]\) or \([c,b]\)) is bounded. Specifically, \(\int_a^c f(x)\,dx\) is defined as \(\lim_{t\to c^-} \int_a^t f(x)\,dx\), while \(\int_{c}^b f(x)\,dx\) is defined as \(\lim_{t\to c^+} \int_t^b f(x)\,dx\).