Question

If the integral [0,3] of f(x)dx=4, the integral [3,6] of f(x)dx=4, and the integral [2,6] of f(x)dx=5, then what does the integral [0,2] of f(x)dx=?

Answer 1

What a great question!

It is `int_0^2 f(x)dx = 3`,

`int_0^3 f(x)dx = 4`, `int_3^6 f(x)dx = 4`, what do I get if I add these two integrals?

I get the integral: `int_0^6 f(x)dx`

And if I subtract this one:

`int_2^6 f(x)dx = 5`

from the sum I found above, what do I get?