Hello Seong,
If you check the documentation for fminbnd, it says that it only looks for a local minimum. It can't guarantee that this is the correct global minimum across the boundary.
On the other hand, the Global Optimization Toolbox is made for finding the global solution instead of local solutions. Since this is a simple 1-D problem, you can easily solve it with a GlobalSearch object, simply following the example on the doc page.
problem = createOptimProblem('fmincon', ...
'objective', absohandle, ...
'x0', 1, 'lb', 0, 'ub', 2);
gs = GlobalSearch;
[x, f] = run(gs, problem)
Alternatively, you could iterate over the range in small increments with fminbnd, then pick the lowest point out of those results. Or do an initial spread of a 100 points or something and calculate the values, picking the bounds based on the lowest points discovered there. But global optimization methods are far more likely to produce the correct result.
-Cam
