Evaluate the integral by interpreting it in terms of areas. \[ \int_{-1}^{0}\left(2+\sqrt{1-x^{2}}\right) d x \]

Step 1 ：The integral can be interpreted as the area under the curve of the function \(f(x) = 2 + \sqrt{1 - x^2}\) from \(x = -1\) to \(x = 0\).

Step 2 ：To find this area, we can use the definite integral, which is the fundamental concept of Calculus. The definite integral of a function can be interpreted as the signed area of the region bounded by the function and the x-axis, from \(x = a\) to \(x = b\).

Step 3 ：The area under the curve of the function \(f(x) = 2 + \sqrt{1 - x^2}\) from \(x = -1\) to \(x = 0\) is calculated as \(\frac{\pi}{4} + 2\).

Step 4 ：Final Answer: The area under the curve of the function \(f(x) = 2 + \sqrt{1 - x^2}\) from \(x = -1\) to \(x = 0\) is \(\boxed{\frac{\pi}{4} + 2}\).