Consider the problem of evaluating the definite integral: ${\displaystyle \underset{0}{\overset{1}{}}}\sqrt[\phantom{2}]{4-x^2}dx=?$

$($a$)$ Give the substitution which is used to solve this problem.

$($b$)$ Give the new limits of integration after the substitution is made.

c$)$ Give the numerical answer for the problem.