Building blocks

## Problem

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.

1. $\int_{-4}^{-2}\sqrt{x+5}\,dx$

2. $\int_{0.2}^{1.3}e^{2x}\,dx$

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