hello
yes - error is not initialized , and BTW, you are shadowing a native matlab function error , which is not good pratice (could led to conflicts or wrong output)
also , your while loop will never stop because the error is constant !
the output of your function is always 24
you can put a breakpoint where you compute I = h/3*(y(1) +even_sum + odd_sum + y(end));
even though each individual term on the RHS is evolving , the result remains exactly the same.
I checked the code of your 1/3 simpson rule and it's correct IMHO
in other words , you have demonstrated that doing this integral computation with always refined x vector does not change the integral value
