Question: How to use units in definite integrals

Hello. I'm trying to calculate some RMS values for a school project. I've double and tripple checked that the forms and units are correctly entered, but it keeps giving me a result that is not convertable to the unit that i know it should output.
 

I've uploaded the file aswell as a picture of the project below:

Analyse.mw

Image: here
File on google drive: here

 

File is updated to include the answer from epostma 1299 , and (almost) works like charm (With exception of the possibility to convert the output unit)

Here is an image of my attempt with the piecewise functionality:

Image: here

 

 

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