$\int_0^{f(a)} f^{-1}(t)\,dt + \int_0^a f(t)\,dt = af(a)?$
36093
Show rigorously that the sum of integrals of $f$ and of its inverse is $bf(b)-af(a)$
66404
Prove that:$\int_{a}^{b} f(x) dx = b \cdot f(b) - a \cdot f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) dx$
154612
$\int_{0}^{x} f(t) dt \ge {f(x)}$ holds or not on $[0,1]$
81258
Evaluation of $\int_{-\infty}^\infty \frac{\sin(at)}t\ dt$
119209
Differentiation wrt parameter $\int_0^\infty \sin^2(x)\cdot(x^2(x^2+1))^{-1}dx$
84413
Why is $\int_{-\infty}^\infty |g(x)|\,dx = \int_0^\infty \mu(\{x : |g(x)| \ge t\})\,dt$ true?
4656
Prove that there is a $\delta$ such that $\int_{0}^{1} (f(x))^2dx\leq \delta$$\int_{0}^{1} (f'(x))^2dx$ for all $f$ with these conditions
36697
Proving that $\int_{-b}^{-a}f(-x)dx=\int_{a}^{b}f(x)dx$
33389
What's the minimum of $\int_0^1 f(x)^2 \: dx$, subject to $\int_0^1 f(x) \: dx = 0, \int_0^1 x f(x) \: dx = 1$?
126046
solving the integral $ \int_0^\infty \dfrac{\sin xt}{x(x^2+1)} dx $
89537
$ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant
102764
Let $f(x)=\int_0^1|t-x|t~dt$ for all real $x$. Sketch the graph of $f(x)$, what is the minimum value of $f(x)$
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
63193
Proof that $\vert\int_a^bf(t)dt\vert\le\int_a^b\vert f(t)\vert dt $ for complex integration
105569
If $f$ is integrable in $[a-1,b+1]$, then prove that $\lim \limits_{h\to 0} \ \int_{a}^{b}|f(x+h)-f(x)| ~ dx=0$
158180
An inequality of $\int_0^1 |f(x)|dx$
23522
Exponential integral $ \int_0^\infty \frac{x^t}{\Gamma(t+1)}\text dt$