Can a "skipna" argument be added for Dataset.integrate() and DataArray.integrate()?

Discussed in https://github.com/pydata/xarray/discussions/5283

^{Originally posted by chfite May 9, 2021}
I am using the Dataset.integrate() function and noticed that because one of my variables has a NaN in it the function returns a NaN for the integrated value for that variable. I know based on the trapezoidal rule one could not get an integrated value at the location of the NaN, but is it not possible for it to calculate the integrated values where there were regular values?

Assuming 0 for NaNs does not work because it would still integrate between the values before and after 0 and add additional area I do not want. Using DataArray.dropna() also is not sufficient because it would assume the value before the NaN is then connected to the value after the NaN and again add additional area that I would not want included.

If a "skipna" functionality or something could not be added to the integrate function, does anyone have a suggestion for another way to get around to calculating my integrated area while excluding the NaNs?

Start by locating the Dataset.integrate() and DataArray.integrate() entry points and their existing tests. Review how the trapezoidal integration handles NaN values, then define the skipna behavior so valid segments are integrated without connecting values across missing points. Done means the argument works for both APIs and tests cover the NaN cases described in the issue.