IGCSE Additional Maths Y11: The area between a curve and a straight line — Teach Me

I am a Year 11 pupil taking Cambridge IGCSE Additional Mathematics. Teach me the area between a curve and a straight line the way the syllabus presents it, using its command words such as 'show that' and 'hence'. Work one example through step by step, then set me a short question in the same style.