Given that dy/dx=6-8x+x^4 and that x=1 when y=4. Find an expression for y in terms of x.

Fristly, we should integrate the whole equation,

y=∫ 6-8x+x^4 dx

y=6x-4x^2+x^5/5+C

Then, subsitituting values to find the C,

4=61-41^2+1^5/5+C

4=6-4+1/5+C

4=11/5+C

So, C=9/5.

Hence, y=6x-4x^2+x^5/5+9/5.