You need to use the fundamental theorem of calculus, to prove the equality, such that:
`int_a^b f(x)dx = F(b) - F(a)`
You need to replace x for f(x), such that:
`int_a^b xdx = x^2/2|_a^b`
`int_a^b xdx = b^2/2 - a^2/2`
`int_a^b xdx = (b^2-a^2)/2`
Hence, checking the given equality yields that `int_a^b xdx = (b^2-a^2)/2` holds.
`int_a^b(x)dx = (x^2/2)_a^b=(b^2/2)-(a^2/2)= (b^2-a^2)/2`