Definite integral of Airy function

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I am trying to understand how $\int_{constant}^\infty Ai(x')dx'$ behaves when the inferior limit is properly a constant "1, 3, 8, etc" all the way to $\infty$

I am using the following in matlab

eta01=-1.1379 - 0.6569i;
airy_INT1=integral(@(n) airy(n),eta01,1000000);

Obtaining zero while, if instead of 1000000 I use 100, I get a non-zero value. I used to think that when eta>around 10, the function is effectively almost zero, but it turns out that the integral is quite sensible, isn't it? Is it that I am not understanding something or an issue with the MATLAB integral function?