Take a look at this diagram.

The area of the blue region is \(53\) and the area of the orange region is \(125\).

Use this to explain why \[\int_{15}^{30}3f(2x-45)\,dx=67.\]

Now try to evaluate each of the following integrals.

\(\int_{-4}^{-2}\sqrt{x+5}\,dx\)

\(\int_{0.2}^{1.3}e^{2x}\,dx\)

Give some examples of other functions that you can integrate in this way.