Find the area bounded by the curve `f(x)=x+ sin x and ` its inverse function between the ordinates `x=0" to "x=2pi`.

Explanation

To find the area bounded by the curve \( f(x) = x + \sin x \) and its inverse function between the ordinates \( x = 0 \) and \( x = 2\pi \), we can follow these steps:

### Step 1: Understand the Function and Its Inverse
The function given is \( f(x) = x + \sin x \). To find the area between this function and its inverse, we first need to confirm that \( f(x) \) is a one-to-one function in the interval \( [0, 2\pi] \).

**Hint:** Check the derivative of the function to determine if it is strictly increasing or decreasing.

### Step 2: Find the Derivative
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