Definite Integrals

Evaluate the definite integral $\int_{0}^{1} x \arctan(x) \, dx$.

A particle moves along a line with velocity $v(t) = t e^{-t^2}$ m/s. Find the distance traveled from $t=0$ to $t=2$ seconds.

The rate of water flow into a tank (in gallons per hour) is given by $r(t)=3t^2+2t+1$ for $0\le t\le 2$. How many gallons of water flow into the tank during the first 2 hours?