It is given that $f ( x ) = - 2 x ^ { 2 } + 10$

Consider the following three curves:

(1) $y = f ( x )$

(2) $y = f ( x + 1 )$

(3) the curve $y = f ( x + 1 )$ reflected in the line $y = 6$

The trapezium rule is used to estimate the area under each of these three curves between $x = 0$ and $x = 1$.

State whether the trapezium rule gives an overestimate or underestimate for each of these areas.

\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
 & (1) & (2) & (3) \\
\hline
A & underestimate & underestimate & underestimate \\
\hline
B & underestimate & underestimate & overestimate \\
\hline
C & underestimate & overestimate & underestimate \\
\hline
D & underestimate & overestimate & overestimate \\
\hline
E & overestimate & underestimate & underestimate \\
\hline
F & overestimate & underestimate & overestimate \\
\hline
G & overestimate & overestimate & underestimate \\
\hline
H & overestimate & overestimate & overestimate \\
\hline
\end{tabular}
\end{center}