integral for range in x axis Calculate the area in the shaded region:
${f(x) = x^3 -2x + 7}$
${{{\int_{-1}^2}} f(x) dx = x^4 - x^2 + 7x}$
$= {[(2^4) -(2^2) + 14] - [(-1)^4 - (-1)^2 + 7(-1)]}$
$= [16 - 4 + 14] - [- 7] = 19$
But the answer in the book is $21{3\over 4}$.


HINT:
$$\int ax^3 + bx^2 + cx^1 + d \, \mathrm{d}x$$
is
$$ \frac{a}{4}x^4 + \frac{b}{3}x^3 + \frac{c}{2}x^3 + dx + C $$
You have miscalculated your first term. Everything else is fine. 
