If the trapezium rule is used to estimate the integral \[\int^1_0 f(x)\, dx,\] by splitting the interval \(0 \le x \le 1\) into \(10\) intervals then an **overestimate** of the integral is produced. It follows that

the trapezium rule with \(10\) intervals underestimates \(\int^1_0 2f(x)\, dx\);

the trapezium rule with \(10\) intervals underestimates \(\int^1_0 (f(x)-1)\, dx\);

the trapezium rule with \(10\) intervals underestimates \(\int^2_1 f(x-1)\, dx\);

the trapezium rule with \(10\) intervals underestimates \(\int^1_0 (1-f(x))\, dx\).

How is each function related to the original function \(f(x)\)? What transformation do we have to apply to \(f(x)\) to get the new function each time?