how to find CVaR/AVaR for triangular fuzzy no

While going through different methods of risk measure i came across AVaR/CVaR, while i was calculating AVaR/CVaR in credibilistic environment using VaR, i got stuck in the calculations

eg. For triangular fuzzy numbers $A =(a1,a2,a3)$ $$VaR(\alpha)= 2*(a1-a2)*\alpha -a1;$$ $$\alpha \leq 0.5$$ $$= 2*(a2-a3)*\alpha +a3-2*a2;$$$$\alpha >0.5$$

Now, $$AVaR(\alpha) = (1/\alpha) \int_0^\alpha Var(\beta)d\beta$$

which somehow results in $$AVaR(\alpha)= (a1-a2)*\alpha -a1;$$$$\alpha \leq 0.5$$ $$= (a2-a3)*\alpha +a3-2*a2-1/4*\alpha(a1-2*a2+a3)$$$$\alpha >0.5$$

Plz help me wd d term $$-1/4*\alpha(a1-2*a2+a3).$$ How to get it?