RMS value of a line to neutral voltage on a three phase inverter
The actual definition of RMS voltage should lead you to the right thing to integrate

$$
Vrms = \sqrt{\frac1T\int_0^T V(t)^{2}}dt\,.
$$

what you wrote is actually fine... but it is only half you don't have the amounts from the part that is negative since it is identical to the positive I guess your T/6 common factor is missing a two for your calculation to be correct, assuming that each rectangle is T/3 on the bottom is correct. 

if you develop that I get
$$
\frac{2Uo^2}{9}
$$

you can just simplify the Ts and add up the Uo squared factors, even the six cancels out. 

edit: changed the Vrms formula to be a bit easier to understand.