How many humans and horses were there?
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Find where the curve intersects the <em>x</em>-axis; this happens when <em>y</em> = 0:
<em>y</em> = <em>t</em> - <em>t</em> ² = 0 → <em>t</em> (1 - <em>t</em> ) = 0 → <em>t</em> = 0, <em>t</em> = 1
Then the area of the bounded region is
(you can compute the integral by parts)