integrate 

Let us first integrate without limit,

I = int (2 sec²x + x³ + 2). dx

I = 2 tanx + (1/4)x⁴ + 2x

Now put the limits,

So, I = 2 (tan(pi/4) - tan0) + (1/4) ((pi/4)⁴ - 0) + 2(pi/4 - 0)

I = 2 + (1/4) (pi/4)⁴ + pi/2 (Ans)..........

 hello dear

Now by 2nd fundamental theorem of calculus,