3
\includegraphics[max width=\textwidth, alt={}, center]{268b605f-eb86-40df-946a-210da1355e83-2_686_967_998_589} The diagram shows the curve with equation \(y = \mathrm { e } ^ { x ^ { 2 } }\), for \(0 \leqslant x \leqslant 1\). The region under the curve between these limits is divided into four strips of equal width. The area of this region under the curve is \(A\).

1. By considering the set of rectangles indicated in the diagram, show that an upper bound for \(A\) is 1.71 .
2. By considering an appropriate set of four rectangles, find a lower bound for \(A\).