Answer
$\int_{0}^{1} \sqrt{4-x^2}dx$.
Work Step by Step
By using the definition of the definite integral, P is a partition of [0,1], therefore the lower and upper limits of the integration are 0 and 1. $f(c_{k})=\sqrt{4-c_{k}^2}$ is the function in the additive of the Riemann sums, therefore $f(x)=\sqrt{4-x^2}$. Therefore the solution is: $\int_{0}^{1} \sqrt{4-x^2}dx$.
