Explain why the following statement is true or false:

The area of the region enclosed by the curves $y=sinx$ and $y=cosx$ on the interval $[0,\frac{}{2}]$ is ${\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}(cosx-sinx)dx$

$2.$ Sketch a solid of revolution whose volume by the disk method is given by the following integral: ${\displaystyle \underset{0}{\overset{2}{}}}(x^2+2x+1)dx$

Indicate the function that generates the solid. Solutions are not unique.