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1. [Maximum mark: 6]

The functions $f$ and $g$ are both defined for $-1 \leq x \leq 0$ by
$f(x) = 1 - x^2$
$g(x) = e^{2x}$.

The graphs of $f$ and $g$ intersect at $x = a$ and $x = b$, where $a < b$.

(a) Find the value of $a$ and the value of $b$. [3]

(b) Find the area of the region enclosed by the graphs of $f$ and $g$. [3]