It helps if you have a visual of what is going on. First we find the intersection points to determine the limits of integration:
This is impossible to solve algebraically so you're going have to obtain the intersection points via your graphing calculator. Let's call these intersection points x = a, 0, and b.
If you graph it out, you'll see y = 2x is greater than 0.3x + 5sin x over the interval and the other way around for the interval . (Remember, area enclosed by two curves is given by the integral of the upper minus the lower function) So,