Answer
$\frac{T^5}{5} - 4T^2 + 7T $
Work Step by Step
$\int^T_{0}(x^4-8x+7)dx$
$=[\frac{x^5}{5} - 4x^2 + 7x] ^T_{0}$
Sub in the bounds and subtract the lower bound (0) from the upper bound (T):
$=[\frac{(T)^5}{5} - 4(T)^2 + 7(T)] - [\frac{(0)^5}{5} - 4(0)^2 + 7(0)] $
$=\frac{T^5}{5} - 4T^2 + 7T - 0$
$=\frac{T^5}{5} - 4T^2 + 7T $.