If a function $f$ is integrable on $[a,b]$, prove that it is integral on $[a,c]$ and $[c,b]$ and that $\int_a^b f = \int_a^c f + \int_c^b f$
115131
Proof that sum of integrals of same function on adjacent intervals equals the integral over both intervals
146921
If |f| is Riemann integrable, then f is Riemann integrable???
22864
Show that $\int_{a}^{b} |f|^2\le\frac{(b-a)^2}{2}\int_{a}^{b} |f'|^2$
157715
Proving $f$ is Lebesgue integrable iff $|f|$ is Lebesgue integrable.
149399
Given continuous $f$ and $g$, there exists $c \in (a,b)$ such that $\int_{a}^{c} f(x) \ \mathrm dx = \int_{c}^{b} g(x) \ \mathrm dx$
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
36697
Proving that $\int_{-b}^{-a}f(-x)dx=\int_{a}^{b}f(x)dx$
25996
Using the definition of Riemann integrability, prove that $f $is Riemann integrable on $[0,1]$
58647
Show that $f$ is integrable and $\int_{I} f=0$
63193
Proof that $\vert\int_a^bf(t)dt\vert\le\int_a^b\vert f(t)\vert dt $ for complex integration
92376
Let $f:A \rightarrow B$ and C ⊂A. Define f[C]={b∈B: b=f(a) for some a∈C}. Prove or disprove each of the statement
18261
Prove $\int_{a}^{b}{f(x)dx}>0$.
114982
How do I get that $|\int_a^b f| \le \int_a^b |f|$?
54266
Prove that $\int_a^b \left( \int_c^d f(x,y)dy\right) dx=\int_c^d \left( \int_a^b f(x,y)dx\right) dy$
98344
Prove that $\int_0^1[f''(x)]^2dx\ge4.$
30940
Prove the integral of $f$ is positive if $f ≥ 0$, $f$ continuous at $x_0$ and $f(x_0)>0$
21586
Prob. 7 (a), Chap. 6, in Baby Rudin: If $f$ is integrable on $[c, 1]$ for every $c>0$, then $\int_0^1 f(x) \ \mathrm{d}x = $ . . .