If $f:[a,b]\to\mathbb{R}$ is Riemann-integrable then it is continuous at a point.
57282
A Riemann integrable function must have infinitely many points of continuity
93021
$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
44144
If $f:[a,b]\to \mathbb R$ is continuous then so is $\max_{t\in [a,x]}f(t)$?
30219
Sufficient condition(s) for $f'$ to be Riemann integrable
146813
Riemann integrability of continuous function defined on closed interval
124444
If $f$ s discontinuous at $x_0$ but $g$ is continuous there, then $f+g$?
113975
Let $f:\mathbb{R}\to\mathbb{R}$, $f(kx)=f(x)$. Show that if $f$ is continuous at $0$ then $f$ is a Constant function
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
8836
If $f$ is continuous on $[a , b]$ and $\int_a^b f(x) p(x)dx = 0$ then $f = 0$
152784
$f \in {\mathscr R[a,b]} \implies f $ has infinitely many points of continuity.
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
95429
If $f$ is continuous with $ \int_0^{\infty}f(t)\,dt<\infty$ then which are correct?
122160
$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$?
136011
Must $f$ be continuous?
145919
If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.
13765
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
146921
If |f| is Riemann integrable, then f is Riemann integrable???