Consider the function g(x) = x^2 +3
There is a diagram and the area under the curve from x=0 to x=1 is approximated by the sum of the area of the two trapeziums.
How do I find this approximation?

Do you have a diagram, at least in your mind? So, if you need two trapeziums, take two trapeziums standing vertically. Both will have a base of 0.5 but different heights.

You know the formula for the area of a trapezium, don't you?

Area of Trapezium = 1/2 x (sum of parallel sides) x perpendicular height

here, the 'height' will be the base. And the slant at the top of the trapezium should be as close as possible to the curve.

Hope it helped!:)