How is $\int f(x) dx$ different from $\int_0^x f(t)dt$?
102059
Understanding integrals double meaning
63193
Proof that $\vert\int_a^bf(t)dt\vert\le\int_a^b\vert f(t)\vert dt $ for complex integration
61133
Show that $\int|f(x)|dx=\int_0^\infty m(E_\alpha)d\alpha$
72039
Compute $\int_0^\infty\frac{\cos(xt)}{1+t^2}dt$
40047
Is $\int_a^b f(x) dx = \int_{f(a)}^{f(b)} f^{-1}(x) dx$?
157608
One-sided limits of $f'(x)$ at a point vs. one-sided limits of the difference quotient at that point
37015
Prove $\int_X |f|^p=p\int^{\infty}_{0} t^{p-1}\mu({x: |f(x)>t}) dt\,$
137664
What exactly is $F$ in $W = \int_{a}^{b} F dx$?
18261
Prove $\int_{a}^{b}{f(x)dx}>0$.
34790
Find $f(1)$ from equation $\int_{0}^{x}f(t)dt = x+\int_{x}^{1}tf(t)dt$
144146
find a $\int_{x}^{g(x)} f(t)\,dt = 1$
11757
How can I compute the integral $\int_{0}^{\infty} \frac{dt}{1+t^4}$?
1626
How do we prove $\int_I\int_x^1\frac{1}{t}f(t)\text{ dt}\text{ dx}=\int_If(x)\text{ dx}$
6892
Why is it not true that $\int_0^{\pi} \sin(x)\; dx = 0$?
90369
Does $\int_a^bf(x) = 0$ imply $f(x) = 0$ for a Riemann Integral function?
139742
Bounding the integral $\int_{2}^{x} \frac{\mathrm dt}{\log^{n}{t}}$
158180
An inequality of $\int_0^1 |f(x)|dx$