急问(高等微积分)Let a and b be positive numbers.Find the value of ∫

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急问(高等微积分)
Let a and b be positive numbers.Find the value of ∫[ax+b]dx in the following two ways:
a.Using elementary geometry,interpreting ∫[ax+b]dx as an area.
b.Using the First Fundamental Theorem (Integrating Derivatives).
注:上下界皆为 1 ,0

a）使用面积原理,直线在（0,1）下的图形为梯形,面积为
∫[ax+b]dx =(1/2)*(b+a+b)*1=（1/2）(a+2b)
b)积分
∫[ax+b]dx =(1/2)ax^2+bx在0到1上计算=(1/2)a+b=（1/2）(a+2b)

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