Is $f(x) = x^{-1/2}$ Riemann integrable on [0,1]?
23942
If a function $f(x)$ is Riemann integrable on $[a,b]$, is $f(x)$ bounded on $[a,b]$?
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
138544
For which values of $x$, will $f (x) . f '(x) < 0$?
154264
$f \in C[-1,1]$, Prove ${\lim_{h \to 0^+}}{\int_{-1}^1 \frac{h}{h^2+x^2}f(x)\,dx} = \pi f(0)$
21843
Proving a function is not Riemann integrable
133636
Is $\mathbb Z[X]/(X^2-1)$ a domain?
30860
Prove that $f(x)=0$ in $[-1,1]$.
83966
Does $ \int_0^{\infty}\frac{\sin x}{x}dx $ have an improper Riemann integral or a Lebesgue integral?
68811
If $f$ is Lebesgue integrable on $[0,2]$ and $\int_E fdx=0$ for all measurable set E such that $m(E)=\pi/2$. Prove or disprove that $f=0$ a.e.
54638
Integral $\int^{ \pi /2}_{0} \ln (\sin x)\ dx$
107254
Real analysis question $e^{-1/x^2}$
68746
What is $f(f^{-1}(A))$?
5814
Integrability of Thomae's Function on $[0,1]$.
46310
Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
85750
If $f(x)=\int_{x-1}^x f(s)ds$, is $f$ constant? Periodic?
40047
Is $\int_a^b f(x) dx = \int_{f(a)}^{f(b)} f^{-1}(x) dx$?
33781
Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?