Advanced Maths $-$ integration

Please please help with clear steps and explanation! Thanks a lot!

Ex $10$

The graph of a cubic function f passes through A$(0$;$0),$ B $(5$;$4),$ C$(15$;$3)$ and D$(20$;$0).$ We note A as the area of $$the domain between this graph and the Ox axis for x in $[0$;$20].$

Determine f$(10)$ and A using the fact that Simpson's method gives the exact value of A both by proceeding directly with the interval $[0$;$20]$ and by joining the intervals $[0$;$10]$ and $[10$; $20]$