Prove

I'm thoroughly confused, eureka. I'm not able to make out what's where [7]

Let f(x) = ₀∫^x e^tx-t2dt - e^x2/4₀∫^xe^-t2/4 dt

f'(x) = e^x2-x2 - e^t2/4 e^-t2/4 = 1-1 = 0

Hence f(x) is a constant. We see that f(0) = 0

Hence f(x) = 0 for all x.

Hence ₀∫^x e^tx-t2dt - e^x2/4₀∫^xe^-t2/4 dt = 0 or

₀∫^x e^tx-t2dt = e^x2/4₀∫^xe^-t2/4 dt

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