title: Getting error indicating number is "out of range for ActiveRecord::Type::Integer with limit 4" when attempting to save large(ish) integer value
body: <p>I'm using SQLite + ActiveRecord in my Ruby app, and here's the error I get while trying to write a big number to the integer field:</p>
  
  <blockquote>
    <p>1428584647765 is out of range for ActiveRecord::Type::Integer with
    limit 4</p>
  </blockquote>
  
  <p>But according to the SQLite documentation:</p>
  
  <blockquote>
    <p>The value is a signed integer, stored in 1, 2, 3, 4, 6, or 8 bytes depending on the magnitude of the value.</p>
  </blockquote>
  
  <p><strong>8 bytes is a plenty of space to store the integer 1428584647765, so why does ActiveRecord give me an error? Why does it think that this is a 4-byte field?</strong></p>