normal distribution question

Hi,

I'm trying to find an answer to the following problem. Any help will be greatly appreciated.

I have a normally-distributed variable X with a mean of 1000 and a some variance (let's assume 1).

I choose a range of 970-990 (for the example's sake).

For any X above 990, I receive 20 dollars.

For any X below 970, I receive 0 dollars.

For X between 970 and 990, I receive: X - 970

My question is: what is the function for calculating the mean profit of this example? (Thinking)

Thanks!

Eyal