$|\int \limits_a^b f(x) dx|\leq\int \limits_a^b |f(x)|dx$ for f continuous
69656
Prove or disprove that $\int_a^b |f(x)|\ \mathrm{d}x\geq \big | \int_a^b f(x)\ \mathrm{d}x\big| $
143174
property of continuous function
128171
Proof for Integral Inequality $|\int f| \le \int |f|$ - is it sufficient enough?
74364
Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
158180
An inequality of $\int_0^1 |f(x)|dx$
143695
Is an increasing, bounded and continuous function on $[a,+\infty)$ uniformly continuous?
155475
$\lim\limits_{n\to \infty} \int_0^1 |f(x)-a_nx-b_n| dx=0$ implies $(a_n)_n,(b_n)_n$ are convergent
128495
Integral Inequality $|f''(x)/f(x)|$
92089
If $f:[a,b]\to \mathbb{R}$ is continuous and nonnegative and $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$
145368
How to show $f:Y\to X^{+}$ is continuous?
18261
Prove $\int_{a}^{b}{f(x)dx}>0$.
53726
Prove that if $f$ is a real continuous function such that $|f|\le 1$ then $|\int_{|z|=1} f(z)dz| \le 4$
16109
Prove that $ \int _a^b\:f\left(x\right)\:\:dx\:=\:\int _a^b\:f\left(a+b-x\right)\:\:dx $
145233
How to show $\lim_{n \rightarrow \infty} \int_0^1 n x^n f(x) \; dx = f(1)$ for continuous $f$?
113122
Prove that a continuous real function with finite limits is bounded
106060
If $f$ is continuous and with a limit at infinity then $f$ is uniformly continuous
75735
Let $f$ be a continuous function on an interval around $0$ and let $a_i=f(\frac{1}{i})$ (for large enough $i$)