In a store, the time (in years) when a product is sold is an independent random variable having the following distribution:

\[ f(x)=\left\{\begin{array}{cc} 2 \sin ^{2}(2 \pi x), & 0 \leq x \leq 1 \\ 0, & \text { otherwise } \end{array}\right. \]

The price of the product, \(P(x)\), is time-dependent and is represented as follows:

\[ P(x)=\left\{\begin{array}{cc} 2-\sin ^{2}(2 \pi x), & 0 \leq x \leq 1 \\ 0, & \text { otherwise } \end{array}\right. \]

What is the expected revenue from the product?