Question 430162
The area under the density curve must be 1:

{{{int((a+bx^2), dx, 0,1) = 1}}}

The expectation is 3.75:

{{{int(x(a+bx^2), dx, 0,1) = 3.75}}}, or {{{int((ax+bx^3), dx, 0,1) = 3.75}}}.

Upon integration of the first, we get {{{a+b/3 = 1}}}, or {{{a = 1-b/3}}}.
Upon integration of the second, we get  {{{a/2 + b/4 = 3.75}}}, or

{{{1/2 - b/6 + b/4 = 3.75}}} after substitution.
==> b = 39
==> a = 1-39/3 = -12.