Yes I do. Take infinitely small slices of one entire waveform, square them, add up the squareS of each heights, find the average, then take the square root of the average. This can be done with calculus.

Use the definition of RMS and work from there.

This is a definition and math problem.
If you are a student you should not be asking for a mathematical expression,
You should derive it.

To me that waveform looks like a typical question from an engineering test...
Some hints: split the simple waveform into several functions, then use the RMS definition and integrate yourself through the waveform step by step.

The easiest way to do it is just to use the rms formula for a trapezoid.....

rms = sqrt(D* ((i1^2+ i1.i2 + i2^2)/3) )

split the wave into two separate trains of 90 degree triangle waveforms........then call each of these a trapezoid with one side = zero.
Then take the square root of the sum of the squares, and youre done.

I think piecewise integration is far messier than this.

The RMS of a trapezoid waveform is a standard well known rule of thumb in the world of power electronics.......it is of course ultimately derived by integration as you spoke of, but for an engineer to go through that every time he or she came to it, would be a waste of time.......