Here are some instructional resources on improper integrals: the integrals that don’t follow the hypotheses of the Fundamental Theorem of Calculus. The idea is that, even though we are sometimes confronted with integrals that ask us to compute undefined regions (whether infinite or that involve dividing by zero), we can still use limits to evaluate these integrals.
Videos:
Watch PatrickJMT go through some evaluations of improper integrals. There are more examples on his YouTube channel if you’re interested.
Watch MathByFives series on improper integrals. BEWARE: he’s a bit quirky.