A reader would integrate information from multiple sources in the following situations:
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To write a report on a topic - This often requires gathering and synthesizing information from various sources to present a comprehensive overview.
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To solve a problem - This may involve looking at multiple perspectives and data points to come to a well-informed solution.
The other options (defining a challenging word, identifying a point of view, and analyzing a theme) might not necessarily require integration from multiple sources in the same way.