Calculus Integration problem. NO clue

Question is as follows :

Let f be the function satisfying f ' (x) = -3xf(x) for all real numbers x, with f(1) = 4 and lim as x -> infinity of f(x) = 0.

a.) Evaluate the integral of -3xf(x) dx with bounds 1 and infinity.

b.) Use Euler's method, starting at x = 1 with a step size of .5 to approximate f(2)

c.) Write an expression for y = f(x) by solving the differential equation dy/dx = -3xy with the initial condition f(1) = 4

I dont really need help with b, once I figure out the equation I can do that one. But A and C have me completely stumped.