You do not need to show any work for this problem.

$($a$)(2$ points$)$ Write ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\sqrt[\phantom{2}]{x^{2}1}dx$ using left endpoints and the limit definition of the integral $($do not evaluate the limit$).$

$($b$)(2$ points$)$ Let $v(t)=t-1$ be a velocity function for $0t2.$ Write the integral for the total distance traveled during this time.

$($c$)(2$ points$)$ Suppose ${\displaystyle \underset{0}{\overset{1}{}}}f(x)dx=10$ and ${\displaystyle \underset{1}{\overset{2}{}}}f(x)dx=13,$ what is ${\displaystyle \underset{0}{\overset{2}{}}}3f(x)dx?$