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What Is an Improper Integral?

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Explanations 1

An improper integral generally looks like this (this is called improper Riemann integral of the first kind): lim⁡a→∞∫baf(x)\lim_{a \to \infty} \int_b^a f(x)a→∞lim∫baf(x) or th…
By Jiazhen Tan, Alex Federspiel

Problems 3

Evaluate lim⁡a→∞∫1a1x2 dx\lim_{a \to \infty} \int_{1}^{a} \frac{1}{x^2}\,dxa→∞lim∫1ax21dx
Is ∫01sin⁡x dx\int_{0}^{1} \sin{x}\,dx∫01sinxdx an improper integral?
Is ∫011x dx\int_{0}^{1} \frac{1}{x}\,dx∫01x1dx an improper integral? If no, why? If so, what kind?