How to save variables from multiple function iterations

I have this functions that computes the area under the curve of a function to a certain accuracy (tolerance):

function area = adaptQuad(f,a,b,tol)
% code that finds the first approximations over the intial interval [a,b]
%  approx2 is always more accurate than approx1 

% approx1;
% approx2;

% initial step size 
h = (b-a)/2;


    if abs(approx1 - approx2) < tol
         % the new interval  'worked'
        area = approx2;
        
    else
        % if the accuracy isn't met, the function calls itself, dividing the interval in half
        area = adaptQuad(f,a,a+h,tol/2) + adaptQuad(f,a+h,b,tol/2);
        
    end

end

The function first tests [a,b], then loops until it finds a small enough interval [a,x] that meets the tolerance, and then moves forward to test the remaining part of the interval [x,x+h].

If you output the intervals as the function runs, it would look something like

%intial interval [a,b] = [-1,1]

[-1,1] % not accurate enough, need smaller interval
[-1,0] % Accuracy met, now test the remaining interval

[0,1] % not accurate enough
[0,0.5] % not accurate enough
[0,0.25] % Accuracy met, now test the remaining interval

[0.25,0.5] % Accuracy met, now test the remaining interval
[0.5,1]    % Accuracy met, end of initial interval

I want to save each interval where the accuracy was met into a ix2 matrix. Where i is the number of times the if statement is met.

if abs(approx1-approx2) < tol
    
    area = approx2;
    
    ints(i,1) = a;
    ints(i,2) = b;
    
end

However, I don't know how to initialize this matrix, or keep the count of i. Any suggestions?

[Walter Roberson]

http://matlab.wikia.com/wiki/FAQ#How_can_I_share_data_between_callback_functions_in_my_GUI.28s.29.3F