Example where $\int_{\text{Int} S} f$ exists and $\int_S f$ does not.
106843
Give an example where $\int_{\bar A} f$ exists but $\int_A f$ does not for a continuos $f$ on a bounded open subset $A$ of $\mathbb{R}^n $
101546
Lebesgue integral $\int_{(0, \infty)} \frac{\sin x}{x} dm$ doesn't exist but improper Riemann integral exists
7010
Example of two non-isomorphic fields which embed inside each other
113385
Example of $f,g: [0,1]\to[0,1]$ and Riemann-integrable, but $g\circ f$ is not?
127049
Can a function be Riemann integrable, but not Lebesgue integrable?
12639
Example of primitive function which isn't Riemann-integrable on a closed interval [0,1]
158940
Give an example of a continuous function $f : [0, ∞) \mapsto [0, ∞)$ such that $\int_{0}^{\infty}f(x)dx$ exists but $f$ is unbounded.
114773
counterexamples on modules
28272
Does such localization of integral extension preserve inclusion?
105769
Prove that $\exists a, b\in(0,1)$ such that $\int_0^{a} xf(x)dx=0\text{ and }\int_0^bxf(x)dx=\frac{b^2f(b)}{2}.$
135610
How to give an example of a $f$ differentiable in a deleted neighborhood of $x_0$ such that $\lim_{x\to x_0}f^\prime(x)$ doesn't exist?
51278
Theorems with an extraordinary exception or a small number of sporadic exceptions
72506
An example s.t. $E(E(X|\mathcal F_1)|\mathcal F_2)\neq E(E(X|\mathcal F_2)|\mathcal F_1)$
138481
$f(x)=x/1$ is not injective?
61267
List of functions not integrable in elementary terms
28452
Statement that is provable in $ZFC+CH$ yet unprovable in $ZFC+\lnot CH$
147722
Is there a nice example of integral domain $R$ and $s,t \in R$, with $Rs \cap Rt$ not principal but lcm($s,t$) exists?