The following Sage code
<code>
var('u')
integrate(-1/8*(u - 2*min_symbolic(-1/2*u - 1/2, 1/2*u - 1/2) - 1)^2 + 1/2*(min_symbolic(0, u) + 1)^2,u,-1,1)
</code>
produces 1/2 as a (correct) result with SageMath 8.3 (running with Software Environment Ubuntu 18.04 @ 2018-08-27 in CoCalc).
With SageMath 9.3 (running with SE Ubuntu 20.04 in CoCalc) the integral doesn't get resolved at all.