To find the area bounded by the two curves, we need to find the x-values where the two curves intersect.

Setting the two equations equal to each other, we have:

sin(2x) = 0.2x + 0.3

To solve this equation, we can use numerical methods or graphing software. By graphing the two equations, we can see that they intersect at approximately x = -0.5 and x = 1.5.

Now, we can integrate the difference between the two curves over the interval [-0.5, 1.5] to find the area:

A = ∫[a,b] (0.2x + 0.3 - sin(2x)) dx

Using the fundamental theorem of calculus, we can find the antiderivative of the integrand:

A = [0.1x^2 + 0.3x + (-0.5)cos(2x)] from -0.5 to 1.5

Evaluating the antiderivative at the upper and lower limits, we have:

A = (0.1(1.5)^2 + 0.3(1.5) + (-0.5)cos(2(1.5))) - (0.1(-0.5)^2 + 0.3(-0.5) + (-0.5)cos(2(-0.5)))

Simplifying this expression, we find:

A ≈ 0.675

Therefore, the approximate area bounded by y = sin(2x) and y = 0.2x + 0.3 is 0.675 square units.