If $f(x) = |5x - 3|$ is defined on interval $[0, 1]$, then the value of $\int_0^1 f(x)\,dx$ is...

The value of integral $\int_0^\infty \dfrac{1}{1 + e^x}\,dx$ is...

If $f(x)$ is an antiderivative of $\dfrac{x + 1}{\sqrt{x - 1}}$ with respect to $x$, then value of $f(5) - f(2)$ is...

The area (in sq. units) of the region bounded by the curve $y = 2x - x^2$ and the X-axis is...