Derive location and spread

Integrate xf(x) to obtain E(X)=(a+b)/2. Integrate x²f(x) to obtain E(X²)=(a²+ab+b²)/3. Subtract the squared mean to get variance (b-a)²/12. The density shape is rectangular and symmetric about the midpoint. The model assumes no preferred location inside its support; a stated maximum alone does not establish a uniform model.