I dont know if its suitable here or on Math SE, Most of the times, when I watched online lectures most lecturers say that if we cant solve a integral exactly we can always numerically integrate it. (E.g. in central force problem the orbit where we find $\theta(r)$ or $r(\theta)$ is pretty difficult to compute and professor said that if needed we can always integrate it numerically if we cannot do it exactly)

So is it always possible to numerically integrate? Is there any example in physics where it not possible to integrate numerically or any integral which cannot be even integrated numerically? Is there any limitation of numerical integration?