Problem is to determine if following expression is inner product over space of continuous functions of form: $$ f: [-1,2] \rightarrow \mathbb{C}$$ define:
$$(i) <f, g> = \int_{-1}^2 \lvert f(x) + g(x) \rvert dx$$
I know that integral of a product of two functions is inner product: $$(ii)<f,g> = \int_{-1}^1 f(x)g(x)dx$$ Showing linearity in (ii) is one-liner, since two functions under integral sign are multiplied. But in my case (i) there is a sum, so I'm stuck. Thank you!