定积分已知-1≤a≤1,f(a)=∫（上面是1下面是0）(2ax^2-a^2x)dx,求f(a)的值域

因为 F(a) = ∫(2ax^2-a^2x)dx = (2/3)*a*(x^3) - (1/2)*(a^2)*(x^2)
所以 f(a) = F(1) - F(0) = (2/3)*a - (1/2)*a^2 ,-1≤a≤1
f(a)是一条抛物线,对称轴是a = 2/3,开口向下,所以f(a)的最大值是f(2/3) = 2/9,最小值是f(-1)=-7/6
因此,f(a)的值域是[-7/6,2/9]